Class 11 • Physics

Motion in 1D

Chpater-2

161 Questions

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Showing 161 of 161 questions

MediumAiims2018

Assertion A body is momentarily at rest at the instant, if it reverse the direction. Reason A body cannot have acceleration, if its velocity is zero at a given instant of time.

Options:

A) Both Assertion and Reason are correct, Reason is the correct explanation of Assertion

B) Both Assertion and Reason are correct but Reason is not the correct explanation of Assertion

C) Assertion is correct and Reason is incorrect

D) Assertion is incorrect and Reason is correct

MediumAiims2017

What will be the a vs x graph for the following graph?

Options:

MediumAiims2017

In an experiment to measure the height of a bridge by dropping stone into water underneath. If the error in measurement of time is $0.2 \mathrm{~s} at the end of 4 \mathrm{~s}$, then the error in estimation of height of bridge will be (neglect the water resistance, i.e. thrust)

Options:

A) \pm 19.68 \mathrm{~m}

B) \pm 17.22 \mathrm{~m}

C) \pm 7.84 \mathrm{~m}

D) \pm 12.22 \mathrm{~m}

MediumJEE Mains2026

A particle starts moving from time t=0 and its coordinate is given as x(t) = 4t^3 - 3t A. The particle returns to its original position (origin) 0.866 units later B. The particle is 1 unit away from origin at its turning point C. Acceleration of the particle is non-negative D. The particle is 0.5 units away from origin at its turning point E. Particle never turns back as acceleration is non-negative Choose the correct answer from the options given below :

Options:

A) A, C, D Only

B) A, B, C Only

C) C, E Only

D) A, C Only

MediumJEE Mains2026

Water drops fall from a tap on the floor, 5 m below, at regular intervals of time, the first drop strikes the floor when the sixth drop begins to fall. The height at which the fourth drop will be from ground, at the instant when the first drop strikes the ground is \_\_\_\_ m. $ \left(\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^2\right)

Options:

A) 3.8

B) 4.0

C) 4.2

D) 2.5

MediumJEE Mains2026

The velocity (v) - Distance (x) graph is shown in figure. Which graph represents acceleration(a) versus distance ( x ) variation of this system?

Options:

MediumJEE Mains2026

A paratrooper jumps from an aeroplane and opens a parachute after 2 s of free fall and starts deaccelerating with 3 \mathrm{~m} / \mathrm{s}^2. At 10 m height from ground, while descending with the help of parachute, the speed of paratrooper is 5 \mathrm{~m} / \mathrm{s}. The initial height of the airplane is \_\_\_\_ m. $ \left(\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^2\right)

Options:

A) 92.5

B) 62.5

C) 20

D) 82.5

MediumJEE Mains2025

The displacement x versus time graph is shown below. (A) The average velocity during 0 to 3 s is 10 \mathrm{~m} / \mathrm{s} (B) The average velocity during 3 to 5 s is 0 \mathrm{~m} / \mathrm{s} (C) The instantaneous velocity at \mathrm{t}=2 \mathrm{~s} is 5 \mathrm{~m} / \mathrm{s} (D) The average velocity during 5 to 7 s and instantaneous velocity at \mathrm{t}=6.5 \mathrm{~s} are equal (E) The average velocity from t=0 to t=9 \mathrm{~s} is zero Choose the correct answer from the options given below :

Options:

A) (B), (C), (D) only

B) (B), (D), (E) only

C) (A), (D), (E) only

D) (B), (C), (E) only

EasyJEE Mains2025

A particle moves along the x-axis and has its displacement x varying with time t according to the equation: $ x=\mathrm{c}_0\left(\mathrm{t}^2-2\right)+\mathrm{c}(\mathrm{t}-2)^2 where \mathrm{c}_0$ and c are constants of appropriate dimensions. Then, which of the following statements is correct?

Options:

A) the acceleration of the particle is 2\left(c+c_0\right)

B) the acceleration of the particle is 2 c_0

C) the acceleration of the particle is 2 c

D) the initial velocity of the particle is 4 c

MediumJEE Mains2025

\text {Which of the following curves possibly represent one-dimensional motion of a particle? } $ Choose the correct answer from the options given below :

Options:

A) A, B and C only

B) A, C and D only

C) A, B and D only

D) A and B only

EasyJEE Mains2025

The velocity-time graph of an object moving along a straight line is shown in the figure. What is the distance covered by the object between t = 0 to t = 4s?

Options:

A) 11 m

B) 30 m

C) 13 m

D) 10 m

EasyJEE Mains2025

The motion of an airplane is represented by velocity-time graph as shown below. The distance covered by airplane in the first 30.5 second is ̱_______ km .

Options:

A) 12

B) 6

C) 3

D) 9

EasyJEE Mains2024

Two cars are travelling towards each other at speed of $20 \mathrm{~m} \mathrm{~s}^{-1} each. When the cars are 300 \mathrm{~m} apart, both the drivers apply brakes and the cars retard at the rate of 2 \mathrm{~m} \mathrm{~s}^{-2}$. The distance between them when they come to rest is :

Options:

A) 25 m

B) 100 m

C) 50 m

D) 200 m

MediumJEE Mains2024

A particle moving in a straight line covers half the distance with speed $6 \mathrm{~m} / \mathrm{s}. The other half is covered in two equal time intervals with speeds 9 \mathrm{~m} / \mathrm{s} and 15 \mathrm{~m} / \mathrm{s}$ respectively. The average speed of the particle during the motion is :

Options:

A) 9.2 m/s

B) 8.8 m/s

C) 10 m/s

D) 8 m/s

MediumJEE Mains2024

A body projected vertically upwards with a certain speed from the top of a tower reaches the ground in $t_1. If it is projected vertically downwards from the same point with the same speed, it reaches the ground in t_2$. Time required to reach the ground, if it is dropped from the top of the tower, is :

Options:

A) \sqrt{\mathrm{t}_1+\mathrm{t}_2}

B) \sqrt{\mathrm{t}_1 \mathrm{t}_2}

C) \sqrt{\frac{\mathrm{t}_1}{\mathrm{t}_2}}

D) \sqrt{\mathrm{t}_1-\mathrm{t}_2}

MediumJEE Mains2024

A train starting from rest first accelerates uniformly up to a speed of $80 \mathrm{~km} / \mathrm{h} for time t, then it moves with a constant speed for time 3 t. The average speed of the train for this duration of journey will be (in \mathrm{km} / \mathrm{h}$) :

Options:

A) 70

B) 40

C) 30

D) 80

EasyJEE Mains2024

A body travels $102.5 \mathrm{~m} in \mathrm{n}^{\text {th }} second and 115.0 \mathrm{~m} in (\mathrm{n}+2)^{\text {th }}$ second. The acceleration is :

Options:

A) 6.25 \mathrm{~m} / \mathrm{s}^2

B) 5 \mathrm{~m} / \mathrm{s}^2

C) 12.5 \mathrm{~m} / \mathrm{s}^2

D) 9 \mathrm{~m} / \mathrm{s}^2

EasyJEE Mains2024

Train A is moving along two parallel rail tracks towards north with speed $72 \mathrm{~km} / \mathrm{h} and train B is moving towards south with speed 108 \mathrm{~km} / \mathrm{h}. Velocity of train B with respect to A and velocity of ground with respect to B are (in \mathrm{ms}^{-1}$):

Options:

A) -50 and -30

B) -50 and 30

C) -30 and 50

D) 50 and -30

MediumJEE Mains2024

The relation between time '$t' and distance 'x' is t=\alpha x^2+\beta x, where \alpha and \beta are constants. The relation between acceleration (a) and velocity (v)$ is :

Options:

A) a=-5 \alpha v^5

B) a=-3 \alpha v^2

C) a=-2 \alpha v^3

D) a=-4 \alpha v^4

EasyJEE Mains2024

A particle is moving in a straight line. The variation of position '$x' as a function of time 't' is given as x=\left(t^3-6 t^2+20 t+15\right) m$. The velocity of the body when its acceleration becomes zero is :

Options:

A) 6 m/s

B) 10 m/s

C) 8 m/s

D) 4 m/s

MediumJEE Mains2024

A body starts moving from rest with constant acceleration covers displacement $S_1 in first (p-1) seconds and \mathrm{S}_2 in first p seconds. The displacement \mathrm{S}_1+\mathrm{S}_2$ will be made in time :

Options:

A) (2 p+1) s

B) (2 p-1) s

C) \left(2 p^2-2 p+1\right) s

D) \sqrt{\left(2 p^2-2 p+1\right)} s

EasyJEE Mains2023

The position of a particle related to time is given by x=\left(5 t^{2}-4 t+5\right) \mathrm{m}. The magnitude of velocity of the particle at t=2 s will be :

Options:

A) 14 \mathrm{~ms}^{-1}

B) 16 \mathrm{~ms}^{-1}

C) 10 \mathrm{~ms}^{-1}

D) 06 \mathrm{~ms}^{-1}

EasyJEE Mains2023

The distance travelled by an object in time $t is given by s=(2.5) t^{2}. The instantaneous speed of the object at \mathrm{t}=5 \mathrm{~s}$ will be:

Options:

A) 5 \mathrm{~ms}^{-1}

B) 12.5 \mathrm{~ms}^{-1}

C) 62.5 \mathrm{~ms}^{-1}

D) 25 \mathrm{~ms}^{-1}

EasyJEE Mains2023

A passenger sitting in a train A moving at $90 \mathrm{~km} / \mathrm{h} observes another train \mathrm{B} moving in the opposite direction for 8 \mathrm{~s}. If the velocity of the train B is 54 \mathrm{~km} / \mathrm{h}$, then length of train B is:

Options:

A) 80 m

B) 200 m

C) 120 m

D) 320 m

MediumJEE Mains2023

Two trains 'A' and 'B' of length '$l' and '4 l' are travelling into a tunnel of length '\mathrm{L}' in parallel tracks from opposite directions with velocities 108 \mathrm{~km} / \mathrm{h} and 72 \mathrm{~km} / \mathrm{h}, respectively. If train 'A' takes 35 \mathrm{~s} less time than train 'B' to cross the tunnel then. length 'L' of tunnel is : (Given \mathrm{L}=60 l$ )

Options:

A) 900 m

B) 1200 m

C) 1800 m

D) 2700 m

EasyJEE Mains2023

A ball is thrown vertically upward with an initial velocity of $150 \mathrm{~m} / \mathrm{s}. The ratio of velocity after 3 \mathrm{~s} and 5 \mathrm{~s} is \frac{x+1}{x}. The value of x is ___________. \left\{\right. take, \left.g=10 \mathrm{~m} / \mathrm{s}^{2}\right\}

Options:

A) -5

B) 10

C) 5

D) 6

EasyJEE Mains2023

From the $\mathrm{v}-t graph shown, the ratio of distance to displacement in 25 \mathrm{~s}$ of motion is:

Options:

A) 1

B) \frac{3}{5}

C) \frac{1}{2}

D) \frac{5}{3}

EasyJEE Mains2023

A person travels $x distance with velocity v_{1} and then x distance with velocity v_{2} in the same direction. The average velocity of the person is \mathrm{v}, then the relation between v, v_{1} and v_{2}$ will be.

Options:

A) \mathbf{V}=\mathbf{V}_{1}+\mathbf{V}_{2}

B) V=\frac{v_{1}+V_{2}}{2}

C) \frac{1}{\mathrm{v}}=\frac{1}{\mathrm{v}_{1}}+\frac{1}{\mathrm{v}_{2}}

D) \frac{2}{\mathrm{~V}}=\frac{1}{\mathrm{v}_{1}}+\frac{1}{\mathrm{v}_{2}}

EasyJEE Mains2023

The position-time graphs for two students A and B returning from the school to their homes are shown in figure. (A) A lives closer to the school (B) B lives closer to the school (C) A takes lesser time to reach home (D) A travels faster than B (E) B travels faster than A Choose the correct answer from the options given below :

Options:

A) (A), (C) and (D) only

B) (A) and (E) only

C) (A), (C) and (E) only

D) (B) and (E) only

EasyJEE Mains2023

Given below are two statements Statement I : Area under velocity- time graph gives the distance travelled by the body in a given time. Statement II : Area under acceleration- time graph is equal to the change in velocity- in the given time. In the light of given statements, choose the correct answer from the options given below.

Options:

A) Both Statement I and Statement II are False.

B) Both Statement I and Statement II are true.

C) Statement I is incorrect but Statement II is true.

D) Statement I is correct but Statement II is false.

EasyJEE Mains2023

A particle starts with an initial velocity of $10.0 \mathrm{~ms}^{-1} along x-direction and accelerates uniformly at the rate of 2.0 \mathrm{~ms}^{-2}. The time taken by the particle to reach the velocity of 60.0 \mathrm{~ms}^{-1}$ is __________.

Options:

A) 30s

B) 6s

C) 3s

D) 25s

EasyJEE Mains2023

An object moves with speed $v_1,v_2 and v_3$ along a line segment AB, BC and CD respectively as shown in figure. Where AB = BC and AD = 3AB, then average speed of the object will be:

Options:

A) {{{v_1}{v_2}{v_3}} \over {3({v_1}{v_2} + {v_2}{v_3} + {v_3}{v_1})}}

B) {{({v_1} + {v_2} + {v_3})} \over 3}

C) {{({v_1} + {v_2} + {v_3})} \over {3{v_1}{v_2}{v_3}}}

D) {{3{v_1}{v_2}{v_3}} \over {({v_1}{v_2} + {v_2}{v_3} + {v_3}{v_1})}}

EasyJEE Mains2023

A vehicle travels 4 \mathrm{~km} with speed of 3 \mathrm{~km} / \mathrm{h} and another 4 \mathrm{~km} with speed of 5 \mathrm{~km} / \mathrm{h}, then its average speed is

Options:

A) 3.75 \mathrm{~km} / \mathrm{h}

B) 4.25 \mathrm{~km} / \mathrm{h}

C) 3.50 \mathrm{~km} / \mathrm{h}

D) 4.00 \mathrm{~km} / \mathrm{h}

MediumJEE Mains2023

Match Column-I with Column-II : Column-I($x-t graphs) Column-II(v$-t graphs) A. I. B. II. C. III. D. IV. Choose the correct answer from the options given below:

Options:

A) A- II, B-III, C-IV, D-I

B) A- II, B-IV, C-III, D-I

C) A- I, B-III, C-IV, D-II

D) A- I, B-II, C-III, D-IV

EasyJEE Mains2023

The distance travelled by a particle is related to time t as $x=4\mathrm{t}^2$. The velocity of the particle at t=5s is :-

Options:

A) \mathrm{25~ms^{-1}}

B) \mathrm{20~ms^{-1}}

C) \mathrm{8~ms^{-1}}

D) \mathrm{40~ms^{-1}}

EasyJEE Mains2023

A car travels a distance of '$x' with speed v_1 and then same distance 'x' with speed v_2$ in the same direction. The average speed of the car is :

Options:

A) {{{v_1}{v_2}} \over {2({v_1} + {v_2})}}

B) {{2{v_1}{v_2}} \over {{v_1} + {v_2}}}

C) {{2x} \over {{v_1} + {v_2}}}

D) {{{v_1} + {v_2}} \over 2}

EasyJEE Mains2023

The velocity time graph of a body moving in a straight line is shown in the figure. The ratio of displacement to distance travelled by the body in time 0 to 10s is :

Options:

A) 1 : 1

B) 1 : 3

C) 1 : 4

D) 1 : 2

MediumJEE Mains2022

A juggler throws balls vertically upwards with same initial velocity in air. When the first ball reaches its highest position, he throws the next ball. Assuming the juggler throws n balls per second, the maximum height the balls can reach is

Options:

A) g/2n

B) g/n

C) 2gn

D) g/2n2

EasyJEE Mains2022

A ball is released from a height h. If $t_{1} and t_{2} be the time required to complete first half and second half of the distance respectively. Then, choose the correct relation between t_{1} and t_{2}$.

Options:

A) t_{1}=(\sqrt{2}) t_{2}

B) t_{1}=(\sqrt{2}-1) t_{2}

C) t_{2}=(\sqrt{2}+1) t_{1}

D) t_{2}=(\sqrt{2}-1) t_{1}

MediumJEE Mains2022

A ball is thrown up vertically with a certain velocity so that, it reaches a maximum height h. Find the ratio of the times in which it is at height $\frac{h}{3}$ while going up and coming down respectively.

Options:

A) \frac{\sqrt{2}-1}{\sqrt{2}+1}

B) \frac{\sqrt{3}-\sqrt{2}}{\sqrt{3}+\sqrt{2}}

C) \frac{\sqrt{3}-1}{\sqrt{3}+1}

D) \frac{1}{3}

EasyJEE Mains2022

If $\mathrm{t}=\sqrt{x}+4, then \left(\frac{\mathrm{d} x}{\mathrm{~d} t}\right)_{\mathrm{t}=4}$ is :

Options:

A) 4

B) zero

C) 8

D) 16

EasyJEE Mains2022

A NCC parade is going at a uniform speed of $9 \mathrm{~km} / \mathrm{h} under a mango tree on which a monkey is sitting at a height of 19.6 \mathrm{~m}. At any particular instant, the monkey drops a mango. A cadet will receive the mango whose distance from the tree at time of drop is: (Given g=9.8 \mathrm{~m} / \mathrm{s}^{2}$ )

Options:

A) 5 m

B) 10 m

C) 19.8 m

D) 24.5 m

MediumJEE Mains2022

The velocity of the bullet becomes one third after it penetrates 4 cm in a wooden block. Assuming that bullet is facing a constant resistance during its motion in the block. The bullet stops completely after travelling at (4 + x) cm inside the block. The value of x is :

Options:

A) 2.0

B) 1.0

C) 0.5

D) 1.5

EasyJEE Mains2022

A bullet is shot vertically downwards with an initial velocity of $100 \mathrm{~m} / \mathrm{s} from a certain height. Within 10 s, the bullet reaches the ground and instantaneously comes to rest due to the perfectly inelastic collision. The velocity-time curve for total time \mathrm{t}=20 \mathrm{~s}$ will be: (Take g = 10 m/s2).

Options:

EasyJEE Mains2022

A small toy starts moving from the position of rest under a constant acceleration. If it travels a distance of 10m in t s, the distance travelled by the toy in the next t s will be :

Options:

A) 10 m

B) 20 m

C) 30 m

D) 40 m

EasyJEE Mains2022

Two balls A and B are placed at the top of 180 m tall tower. Ball A is released from the top at t = 0 s. Ball B is thrown vertically down with an initial velocity 'u' at t = 2 s. After a certain time, both balls meet 100 m above the ground. Find the value of 'u' in ms$-1. [use g = 10 ms-$2] :

Options:

A) 10

B) 15

C) 20

D) 30

EasyJEE Mains2022

Two buses P and Q start from a point at the same time and move in a straight line and their positions are represented by ${X_P}(t) = \alpha t + \beta {t^2} and {X_Q}(t) = ft - {t^2}$. At what time, both the buses have same velocity?

Options:

A) {{\alpha - f} \over {1 + \beta }}

B) {{\alpha + f} \over {2(\beta - 1)}}

C) {{\alpha + f} \over {2(1 + \beta )}}

D) {{f - \alpha } \over {2(1 + \beta )}}

MediumJEE Mains2021

Water drops are falling from a nozzle of a shower onto the floor, from a height of 9.8 m. The drops fall at a regular interval of time. When the first drop strikes the floor, at that instant, the third drop begins to fall. Locate the position of second drop from the floor when the first drop strikes the floor.

Options:

A) 4.18 m

B) 2.94 m

C) 2.45 m

D) 7.35 m

MediumJEE Mains2021

A ball is thrown up with a certain velocity so that it reaches a height 'h'. Find the ratio of the two different times of the ball reaching ${h \over 3}$ in both the directions.

Options:

A) {{\sqrt 2 - 1} \over {\sqrt 2 + 1}}

B) {1 \over 3}

C) {{\sqrt 3 - \sqrt 2 } \over {\sqrt 3 + \sqrt 2 }}

D) {{\sqrt 3 - 1} \over {\sqrt 3 + 1}}

MediumJEE Mains2021

The relation between time t and distance x for a moving body is given as t = mx2 + nx, where m and n are constants. The retardation of the motion is : (When v stands for velocity)

Options:

A) 2 mv3

B) 2 mnv3

C) 2nv3

D) 2n2v3

EasyJEE Mains2021

A balloon was moving upwards with a uniform velocity of 10 m/s. An object of finite mass is dropped from the balloon when it was at a height of 75 m from the ground level. The height of the balloon from the ground when object strikes the ground was around :(takes the value of g as 10 m/s2)

Options:

A) 300 m

B) 200 m

C) 125 m

D) 250 m

EasyJEE Mains2021

The instantaneous velocity of a particle moving in a straight line is given as $V = \alpha t + \beta {t^2}, where \alpha and \beta$ are constants. The distance travelled by the particle between 1s and 2s is :

Options:

A) 3$\alpha + 7\beta

B) {3 \over 2}\alpha + {7 \over 3}\beta

C) {\alpha \over 2} + {\beta \over 3}

D) {3 \over 2}\alpha + {7 \over 2}\beta

MediumJEE Mains2021

Water droplets are coming from an open tap at a particular rate. The spacing between a droplet observed at 4th second after its fall to the next droplet is 34.3 m. At what rate the droplets are coming from the tap ? (Take g = 9.8 m/s2)

Options:

A) 3 drops / 2 sconds

B) 2 drops / second

C) 1 drop / second

D) 1 drop / 7 seconds

EasyJEE Mains2021

A boy reaches the airport and finds that the escalator is not working. He walks up the stationary escalator in time t1. If he remains stationary on a moving escalator then the escalator takes him up in time t2. The time taken by him to walk up on the moving escalator will be :

Options:

A) {{{t_1}{t_2}} \over {{t_2} - {t_1}}}

B) {{{t_1} + {t_2}} \over 2}

C) {{{t_1}{t_2}} \over {{t_2} + {t_1}}}

D) {t_2} - {t_1}

MediumJEE Mains2021

The velocity $- displacement graph of a particle is shown in the figure.The acceleration -$ displacement graph of the same particle is represented by :

Options:

EasyJEE Mains2021

The position, velocity and acceleration of a particle moving with a constant acceleration can be represented by :

Options:

EasyJEE Mains2021

The velocity of a particle is v = v0 + gt + Ft2. Its position is x = 0 at t = 0; then its displacement after time (t = 1) is :

Options:

A) v0 + g + f

B) v0 + ${g \over 2} + {F \over 3}

C) v0 + 2g + 3F

D) v0 + ${g \over 2}$ + F

MediumJEE Mains2021

A rubber ball is released from a height of 5 m above the floor. It bounces back repeatedly, always rising to ${{81} \over {100}} of the height through which it falls. Find the average speed of the ball. (Take g = 10 ms-$2)

Options:

A) 2.50 ms$-$1

B) 3.0 ms$-$1

C) 2.0 ms$-$1

D) 3.50 ms$-$1

MediumJEE Mains2021

A car accelerates from rest at a constant rate $\alpha for some time after which it decelerates at a constant rate \beta$ to come to rest. If the total time elapsed is t seconds, the total distance travelled is :

Options:

A) {{4\alpha \beta } \over {(\alpha + \beta )}}{t^2}

B) {{2\alpha \beta } \over {(\alpha + \beta )}}{t^2}

C) {{\alpha \beta } \over {2(\alpha + \beta )}}{t^2}

D) {{\alpha \beta } \over {4(\alpha + \beta )}}{t^2}

MediumJEE Mains2021

The velocity-displacement graph describing the motion of bicycle is shown in the figure.The acceleration-displacement graph of the bicycle's motion is best described by :

Options:

EasyJEE Mains2021

A scooter accelerates from rest for time t1 at constant rate a1 and then retards at constant rate a2 for time t2 and comes to rest. The correct value of ${{{t_1}} \over {{t_2}}}$ wil be :

Options:

A) {{{a_1} + {a_2}} \over {{a_2}}}

B) {{{a_1} + {a_2}} \over {{a_1}}}

C) {{{a_2}} \over {{a_1}}}

D) {{{a_1}} \over {{a_2}}}

MediumJEE Mains2021

A stone is dropped from the top of a building. When it crosses a point 5 m below the top, another stone starts to fall from a point 25 m below the top. Both stones reach the bottom of building simultaneously. The height of the building is :

Options:

A) 50 m

B) 25 m

C) 45 m

D) 35 m

MediumJEE Mains2021

An engine of a train, moving with uniform acceleration, passes the signal-post with velocity u and the last compartment with velocity v. The velocity with which middle point of the train passes the signal post is :

Options:

A) {{u + v} \over 2}

B) \sqrt {{{{v^2} - {u^2}} \over 2}}

C) {{v - u} \over 2}

D) \sqrt {{{{v^2} + {u^2}} \over 2}}

EasyJEE Mains2021

If the velocity-time graph has the shape AMB, what would be the shape of the corresponding acceleration-time graph?

Options:

MediumJEE Mains2020

The velocity (v) and time (t) graph of a body in a straight line motion is shown in the figure. The point S is at 4.333 seconds. The total distance covered by the body in 6 s is :

Options:

A) 12 m

B) 11 m

C) {{49} \over 4}$ m

D) {{37} \over 3}$ m

MediumJEE Mains2020

A helicopter rises from rest on the ground vertically upwards with a constant acceleration g. A food packet is dropped from the helicopter when it is at a height h. The time taken by the packet to reach the ground is close to : [g is the acceleration due to gravity]

Options:

A) t = 3.4$\sqrt {\left( {{h \over g}} \right)}

B) t = 1.8$\sqrt {\left( {{h \over g}} \right)}

C) t = $\sqrt {{{2h} \over {3g}}}

D) t = ${2 \over 3}\sqrt {\left( {{h \over g}} \right)}

MediumJEE Mains2020

A Tennis ball is released from a height h and after freely falling on a wooden floor it rebounds and reaches height ${h \over 2}$. The velocity versus height of the ball during its motion may be represented graphically by : (graph are drawn schematically and on not to scale)

Options:

MediumJEE Mains2020

Train A and train B are running on parallel tracks in the opposite directions with speeds of 36 km/hour and 72 km/hour, respectively. A person is walking in train A in the direction opposite to its motion with a speed of 1.8 km/ hour. Speed (in ms–1) of this person as observed from train B will be close to : (take the distance between the tracks as negligible)

Options:

A) 30.5 ms–1

B) 29.5 ms–1

C) 31.5 ms–1

D) 28.5 ms–1

MediumJEE Mains2019

A particle is moving with speed v = b$\sqrt x along positive x-axis. Calculate the speed of the particle at time t = \tau $(assume that the particle is at origin t = 0)

Options:

A) {{{b^2}\tau } \over {\sqrt 2 }}

B) {{b^2}\tau }

C) {{{b^2}\tau } \over 2}

D) {{{b^2}\tau } \over 4}

MediumJEE Mains2019

The position vector of a particle changes with time according to the relation $\overrightarrow r (t) = 15{t^2}\widehat i + (4 - 20{t^2})\widehat j$ What is the magnitude of the acceleration at t = 1 ?

Options:

A) 50

B) 25

C) 40

D) 100

MediumJEE Mains2019

The position of a particle as a function of time t, is given byx(t) = at + bt2 – ct3 where a, b and c are constants. When the particle attains zero acceleration, then its velocity will be :

Options:

A) a + {{{b^2}} \over {c}}

B) a + {{{b^2}} \over {4c}}

C) a + {{{b^2}} \over {3c}}

D) a + {{{b^2}} \over {2c}}

MediumJEE Mains2019

A particle starts from origin O from rest and moves with a uniform acceleration along the positive x-axis. Identify all figures that correctly represent the motion qualitatively. (a = acceleration, v = velocity, x = displacement, t = time)

Options:

A) (B), (C)

B) (A)

C) (A), (B), (C)

D) (A), (B), (D)

MediumJEE Mains2019

A passenger train of length 60 m travels at a speed of 80 km/hr. Another freight train of length 120 m travels at a speed of 30 km/hr. The ratio of times taken by the passenger train to completely cross the freight train when : (i) they are moving in the same direction , and (ii) in the opposite direction is :

Options:

A) {{25} \over {11}}

B) {3 \over 2}

C) {{11} \over 5}

D) {5 \over 2}

MediumJEE Mains2019

A particle moves from the point $\left( {2.0\widehat i + 4.0\widehat j} \right) m, at t = 0, with an initial velocity \left( {5.0\widehat i + 4.0\widehat j} \right) ms-1. It is acted upon by a constant force which produces a constant acceleration \left( {4.0\widehat i + 4.0\widehat j} \right) ms-$2. What is the distance of the particle from the origin at time 2 s?

Options:

A) 15 m

B) 20\sqrt 2 $ m

C) 10\sqrt 2 $ m

D) 5 m

MediumJEE Mains2019

A particle starts from the origin at time t = 0 and moves along the positive x-axis. The graph of velocity with respect to time is shown in figure. What is the position of the particle at time t = 5s ?

Options:

A) 3 m

B) 9 m

C) 10 m

D) 6 m

MediumJEE Mains2019

In a car race on straight road, car A takes a time t less than car B at the finish and passes finishing point with a speed '$\upsilon ' more than that of car B. Both the cars start from rest and travel with constant acceleration a1 and a2 respectively. Then '\upsilon $' is equal to :

Options:

A) {{2{a_1}{a_2}} \over {{a_1} + {a_2}}}t

B) \sqrt {2{a_1}{a_2}} t

C) \sqrt {{a_1}{a_2}} t

D) {{{a_1} + {a_2}} \over 2}t

MediumJEE Mains2018

All the graphs below are intended to represent the same motion. One of them does it incorrectly. Pick it up.

Options:

MediumJEE Mains2018

An automobile, travelling at $40\, km/h, can be stopped at a distance of 40\, m by applying brakes. If the same automobile is travelling at 80\,$ km/h, the minimum stopping distance, in metres, is (assume no skidding) :

Options:

A) 45\,$ m

B) 100\,$ m

C) 150\,$ m

D) 160\,$ m

MediumJEE Mains2018

The velocity-time graphs of a car and a scooter are shown in the figure. (i) The difference between the distance travelled by the car and the scooter in $15 s$ and (ii) the time at which the car will catch up with the scooter are, respectively.

Options:

A) 112.5 m and 22.5 s

B) 337.5 m and 25 s

C) 112.5 m and 15 s

D) 225.5 m and 10 s

MediumJEE Mains2017

A car is standing 200 m behind a bus, which is also at rest. The two start moving at the same instant but with different forward accelerations. The bus has acceleration 2 m/s2 and the car has acceleration 4 m/s2 . The car will catch up with the bus after a time of :

Options:

A) \sqrt {110} \,s

B) \sqrt {120} \,s

C) 10\,\,\sqrt 2 \,s

D) 15 s

MediumJEE Mains2017

Which graph corresponds to an object moving with a constant negative acceleration and a positive velocity ?

Options:

MediumJEE Mains2017

A body is thrown vertically upwards. Which one of the following graphs correctly represent the velocity vs time?

Options:

MediumJEE Mains2015

Two stones are thrown up simultaneously from the edge of a cliff $240 m high with initial speed of 10 m/s and 40 m/s respectively. Which of the following graph best represents the time variation of relative position of the second stone with respect to the first ? (Assume stones do not rebound after hitting the ground and neglect air resistance, take g = 10m/{s^2}$) (The figures are schematic and not drawn to scale)

Options:

MediumJEE Mains2014

From a tower of height H, a particle is thrown vertically upwards with a speed u. The time taken by the particle, to hit the ground, is n times that taken by it to reach the highest point of its path. The relation between H, u and n is:

Options:

A) 2gH = n2u2

B) gH = (n - 2)2u2

C) 2gH = nu2(n - 2)

D) gH = (n - 2)u2

MediumJEE Mains2011

An object, moving with a speed of 6.25 m/s, is decelerated at a rate given by : ${{dv} \over {dt}} = - 2.5\sqrt v $ where v is the instantaneous speed. The time taken by the object, to come to rest, would be :

Options:

A) 2 s

B) 4 s

C) 8 s

D) 1 s

MediumJEE Mains2009

Consider a rubber ball freely falling from a height $h=4.9 m$ onto a horizontal elastic plate. Assume that the duration of collision is negligible and the collision with the plate is totally elastic. Then the velocity as a function of time and the height as a function of time will be :

Options:

MediumJEE Mains2008

A body is at rest at $x=0. At t=0, it starts moving in the positive x-direction with a constant acceleration. At the same instant another body passes through x=0 moving in the positive x direction with a constant speed. The position of the first body is given by {x_1}\left( t \right) after time 't'; and that of the second body by {x_2}\left( t \right) after the same time interval. Which of the following graphs correctly describes \left( {{x_1} - {x_2}} \right) as a function of time 't'$ ?

Options:

MediumJEE Mains2007

The velocity of a particle is v = v0 + gt + ft2. If its position is x = 0 at t = 0, then its displacement after unit time (t = 1) is

Options:

A) v0 + g/2 + f

B) v0 + 2g + 3f

C) v0 + g/2 + f/3

D) v0 + g + f

MediumJEE Mains2006

A particle located at x = 0 at time t = 0, starts moving along the positive x-direction with a velocity 'v' that varies as $v = \alpha \sqrt x $. The displacement of the particle varies with time as

Options:

A) t2

B) t

C) t1/2

D) t3

MediumJEE Mains2005

The relation between time t and distance x is t = ax2 + bx where a and b are constants. The acceleration is

Options:

A) 2bv3

B) -2abv2

C) 2av2

D) -2av3

MediumJEE Mains2005

A car starting from rest accelerates at the rate f through a distance S, then continues at constant speed for time t and then decelerates at the rate ${f \over 2}$ to come to rest. If the total distance traversed is 15 S, then

Options:

A) S = {1 \over 6}f{t^2}

B) S = ft

C) S = {1 \over 4}f{t^2}

D) S = {1 \over 72}f{t^2}

MediumJEE Mains2005

A parachutist after bailing out falls $50 m without friction. When parachute opens, it decelerates at 2\,\,m/{s^2}. He reaches the ground with a speed of 3 m/s$. At what height, did he bail out?

Options:

A) 182 m

B) 91 m

C) 111 m

D) 293 m

MediumJEE Mains2004

An automobile travelling with speed of 60 km/h, can brake to stop within a distance of 20 m. If the car is going twice as fast, i.e 120 km/h, the stopping distance will be

Options:

A) 60 m

B) 40 m

C) 20 m

D) 80 m

MediumJEE Mains2004

A ball is released from the top of a tower of height h meters. It takes T seconds to reach the ground. What is the position of the ball in ${T \over 3}$ seconds?

Options:

A) {{8h} \over 9}$ meters from the ground

B) {{7h} \over 9}$ meters from the ground

C) {h \over 9}$ meters from the ground

D) {{7h} \over {18}}$ meters from the ground

MediumJEE Mains2003

A car, moving with a speed of 50 km/hr, can be stopped by brakes after at least 6 m. If the same car is moving at a speed of 100 km/hr, the minimum stopping distance is

Options:

A) 12 m

B) 18 m

C) 24 m

D) 6 m

MediumJEE Mains2003

The co-ordinates of a moving particle at any time 't' are given by x = $\alpha $t3 and y = βt3. The speed to the particle at time 't' is given by

Options:

A) 3t\sqrt {{\alpha ^2} + {\beta ^2}}

B) 3{t^2}\sqrt {{\alpha ^2} + {\beta ^2}}

C) {t^2}\sqrt {{\alpha ^2} + {\beta ^2}}

D) \sqrt {{\alpha ^2} + {\beta ^2}}

MediumJEE Mains2002

From a building two balls A and B are thrown such that A is thrown upwards and B downwards ( both vertically with the same speed ). If vA and vB are their respective velocities on reaching the ground, then

Options:

A) {v_B} > {v_A}

B) {v_A} = {v_B}

C) {v_A} > {v_B}

D) their velocities depend on their masses.

MediumJEE Mains2002

Speeds of two identical cars are $u and 4u $ at the specific instant. The ratio of the respective distances in which the two cars are stopped from that instant is :

Options:

A) 1:1

B) 1:4

C) 1:8

D) 1:16

EasyJEE Mains2025

A person travelling on a straight line moves with a uniform velocity v_1 for a distance x and with a uniform velocity v_2 for the next \frac{3}{2} x distance. The average velocity in this motion is \frac{50}{7} \mathrm{~m} / \mathrm{s}. If v_1 is 5 \mathrm{~m} / \mathrm{s} then v_2= __________ \mathrm{m} / \mathrm{s}.

Options:

100

HardJEE Mains2025

Two cars P and Q are moving on a road in the same direction. Acceleration of car P increases linearly with time whereas car Q moves with a constant acceleration. Both cars cross each other at time t = 0, for the first time. The maximum possible number of crossing(s) (including the crossing at t = 0) is ________.

Options:

101

MediumJEE Mains2024

A particle moves in a straight line so that its displacement $x at any time t is given by x^2=1+t^2. Its acceleration at any time \mathrm{t} is x^{-\mathrm{n}} where \mathrm{n}=$ _________.

Options:

102

MediumJEE Mains2024

A body moves on a frictionless plane starting from rest. If $\mathrm{S_n} is distance moved between \mathrm{t=n-1} and \mathrm{t}=\mathrm{n} and \mathrm{S}_{\mathrm{n}-1} is distance moved between \mathrm{t}=\mathrm{n}-2 and \mathrm{t}=\mathrm{n}-1, then the ratio \frac{\mathrm{S}_{\mathrm{n}-1}}{\mathrm{~S}_{\mathrm{n}}} is \left(1-\frac{2}{x}\right) for \mathrm{n}=10. The value of x$ is __________.

Options:

103

EasyJEE Mains2024

A bus moving along a straight highway with speed of $72 \mathrm{~km} / \mathrm{h} is brought to halt within 4 s after applying the brakes. The distance travelled by the bus during this time (Assume the retardation is uniform) is ________ m$.

Options:

104

MediumJEE Mains2024

A particle initially at rest starts moving from reference point x=0 along x-axis, with velocity v that varies as v=4 \sqrt{x} \mathrm{~m} / \mathrm{s}. The acceleration of the particle is __________ \mathrm{ms}^{-2}.

Options:

105

EasyJEE Mains2024

A particle is moving in one dimension (along x axis) under the action of a variable force. It's initial position was 16 \mathrm{~m} right of origin. The variation of its position (x) with time (t) is given as x=-3 t^3+18 t^2+16 t, where x is in \mathrm{m} and \mathrm{t} is in \mathrm{s}. The velocity of the particle when its acceleration becomes zero is _________ \mathrm{m} / \mathrm{s}.

Options:

106

MediumJEE Mains2024

The displacement and the increase in the velocity of a moving particle in the time interval of $t to (t+1) \mathrm{s} are 125 \mathrm{~m} and 50 \mathrm{~m} / \mathrm{s}, respectively. The distance travelled by the particle in (\mathrm{t}+2)^{\mathrm{th}} \mathrm{s}$ is _________ m.

Options:

107

MediumJEE Mains2024

A body falling under gravity covers two points $A and B separated by 80 \mathrm{~m} in 2 \mathrm{~s}. The distance of upper point A from the starting point is _________ \mathrm{m} (use \mathrm{g}=10 \mathrm{~ms}^{-2}$).

Options:

108

MediumJEE Mains2023

For a train engine moving with speed of $20 \mathrm{~ms}^{-1}, the driver must apply brakes at a distance of 500 \mathrm{m} before the station for the train to come to rest at the station. If the brakes were applied at half of this distance, the train engine would cross the station with speed \sqrt{x} \mathrm{~ms}^{-1}. The value of x$ is ____________. (Assuming same retardation is produced by brakes)

Options:

109

EasyJEE Mains2023

A horse rider covers half the distance with $5 \mathrm{~m} / \mathrm{s} speed. The remaining part of the distance was travelled with speed 10 \mathrm{~m} / \mathrm{s} for half the time and with speed 15 \mathrm{~m} / \mathrm{s} for other half of the time. The mean speed of the rider averaged over the whole time of motion is \frac{x}{7} \mathrm{~m} / \mathrm{s}. The value of x$ is ___________.

Options:

110

EasyJEE Mains2023

A tennis ball is dropped on to the floor from a height of 9.8 m. It rebounds to a height 5.0 m. Ball comes in contact with the floor for 0.2s. The average acceleration during contact is ___________ ms$^{-2}. (Given g = 10 ms^{-2}$)

Options:

111

EasyJEE Mains2022

A ball is thrown vertically upwards with a velocity of $19.6 \mathrm{~ms}^{-1} from the top of a tower. The ball strikes the ground after 6 \mathrm{~s}. The height from the ground up to which the ball can rise will be \left(\frac{k}{5}\right) \mathrm{m}. The value of \mathrm{k} is __________. (use \mathrm{g}=9.8 \mathrm{~m} / \mathrm{s}^{2}$)

Options:

112

MediumJEE Mains2022

A particle is moving in a straight line such that its velocity is increasing at 5 ms$-1 per meter. The acceleration of the particle is _____________ ms-2 at a point where its velocity is 20 ms-$1.

Options:

113

EasyJEE Mains2022

A car is moving with speed of $150 \mathrm{~km} / \mathrm{h} and after applying the break it will move 27 \mathrm{~m}$ before it stops. If the same car is moving with a speed of one third the reported speed then it will stop after travelling ___________ m distance.

Options:

114

EasyJEE Mains2022

A car covers AB distance with first one-third at velocity v1 ms$-1, second one-third at v2 ms-1 and last one-third at v3 ms-1. If v3 = 3v1, v2 = 2v1 and v1 = 11 ms-1 then the average velocity of the car is _____________ ms-$1.

Options:

115

MediumJEE Mains2022

A ball is projected vertically upward with an initial velocity of 50 ms$-1 at t = 0s. At t = 2s, another ball is projected vertically upward with same velocity. At t = __________ s, second ball will meet the first ball (g = 10 ms-$2).

Options:

116

EasyJEE Mains2022

A ball of mass 0.5 kg is dropped from the height of 10 m. The height, at which the magnitude of velocity becomes equal to the magnitude of acceleration due to gravity, is ________ m. [Use g = 10 m/s2]

Options:

117

MediumJEE Mains2022

From the top of a tower, a ball is thrown vertically upward which reaches the ground in 6 s. A second ball thrown vertically downward from the same position with the same speed reaches the ground in 1.5 s. A third ball released, from the rest from the same location, will reach the ground in ____________ s.

Options:

118

EasyJEE Mains2021

A particle is moving with constant acceleration 'a'. Following graph shows v2 versus x(displacement) plot. The acceleration of the particle is ___________ m/s2.

Options:

119

MediumJEE Mains2021

If the velocity of a body related to displacement x is given by $\upsilon = \sqrt {5000 + 24x} $ m/s, then the acceleration of the body is .................... m/s2.

Options:

120

MediumJEE Mains2021

Two spherical balls having equal masses with radius of 5 cm each are thrown upwards along the same vertical direction at an interval of 3s with the same initial velocity of 35 m/s, then these balls collide at a height of ............... m. (Take g = 10 m/s2)

Options:

121

MediumJEE Mains2020

The speed verses time graph for a particle is shown in the figure. The distance travelled (in m) by the particle during the time interval t = 0 to t = 5 s will be________.

Options:

122

MediumJEE Mains2020

The distance x covered by a particle in one dimensional motion varies with time t as x2 = at2 + 2bt + c. If the acceleration of the particle depends on x as x–n, where n is an integer, the value of n is __________

Options:

123

HardNEET2025

In some appropriate units, time (t) and position (x) relation of a moving particle is given by t=x^2+x. The acceleration of the particle is

Options:

A) +\frac{2}{(x+1)^3}

B) +\frac{2}{2 x+1}

C) -\frac{2}{(x+2)^3}

D) -\frac{2}{(2 x+1)^3}

124

HardNEET2025

Two cities X and Y are connected by a regular bus service with a bus leaving in either direction every T min. A girl is driving scooty with a speed of 60 \mathrm{~km} / \mathrm{h} in the direction X to Y notices that a bus goes past her every 30 minutes in the direction of her motion, and every 10 minutes in the opposite direction. Choose the correct option for the period T of the bus service and the speed (assumed constant) of the buses.

Options:

A) 10 \mathrm{~min}, 90 \mathrm{~km} / \mathrm{h}

B) 15 \mathrm{~min}, 120 \mathrm{~km} / \mathrm{h}

C) 9 \mathrm{~min}, 40 \mathrm{~km} / \mathrm{h}

D) 25 \mathrm{~min}, 100 \mathrm{~km} / \mathrm{h}

125

MediumNEET2024

A particle is moving along $x-axis with its position (x) varying with time (t) as x=\alpha t^4+\beta t^2+\gamma t+\delta$. The ratio of its initial velocity to its initial acceleration, respectively, is:

Options:

A) 2 \alpha: \delta

B) \gamma: 2 \delta

C) 4 \alpha: \beta

D) \gamma: 2 \beta

126

MediumNEET2024

The velocity $(v)- time (t) plot of the motion of a body is shown below: The acceleration (a)- time (t)$ graph that best suits this motion is :

Options:

127

MediumNEET2023

The position of a particle is given by $\vec{r}(t)=4 t \hat{i}+2 t^2 \hat{j}+5 \hat{k} where \mathrm{t} is in seconds and \mathrm{r} in metre. Find the magnitude and direction of velocity v(t), at t=1 \mathrm{~s}, with respect to \mathrm{x}$-axis

Options:

A) 4 \sqrt{2} \mathrm{~ms}^{-1}, 45^{\circ}

B) 4 \sqrt{2} \mathrm{~ms}^{-1}, 60^{\circ}

C) 3 \sqrt{2} \mathrm{~ms}^{-1}, 30^{\circ}

D) 3 \sqrt{2} \mathrm{~ms}^{-1}, 45^{\circ}

128

MediumNEET2023

A vehicle travels half the distance with speed $v and the remaining distance with speed 2 v$. Its average speed is :

Options:

A) \frac{2 v}{3}

B) \frac{4 v}{3}

C) \frac{3 v}{4}

D) \frac{v}{3}

129

MediumNEET2022

The position-time (x - t) graph for positive acceleration is

Options:

130

MediumNEET2022

The ratio of the distances travelled by a freely falling body in the 1st, 2nd, 3rd and 4th second

Options:

A) 1 : 2 : 3 : 4

B) 1 : 4 : 9 : 16

C) 1 : 3 : 5 : 7

D) 1 : 1 : 1 : 1

131

MediumNEET2022

The displacement-time graphs of two moving particles make angles of 30$^\circ and 45^\circ$ with the x-axis as shown in the figure. The ratio of their respective velocity is

Options:

A) \sqrt3$ : 1

B) 1 : 1

C) 1 : 2

D) 1 : $\sqrt3

132

MediumNEET2021

A small block slides down on a smooth inclined plane, starting from rest at time t = 0. Let Sn be the distance travelled by the block in the interval t = n $- 1 to t = n. The the ratio {{{S_n}} \over {{S_{n + 1}}}}$ is :

Options:

A) {{2n} \over {2n - 1}}

B) {{2n - 1} \over {2n}}

C) {{2n - 1} \over {2n + 1}}

D) {{2n + 1} \over {2n - 1}}

133

MediumNEET2020

A ball is thrown vertically downward with a velocity of 20 m/s from the top of a tower. It hits the ground after some time with a velocity of 80 m/s. The height of the tower is : (g = 10 m/s2)

Options:

A) 340 m

B) 320 m

C) 300 m

D) 360 m

134

MediumNEET2019

The speed of a swimmer in still water is 20 m/s. The speed of river water is 10 m/s and is flowing due east. If he is standing on the south bank and wishes to cross the river along the shortest path, the angle at which he should make his strokes w.r.t. north is given by :

Options:

A) 0o

B) 60

C) 45o west

D) 30o west

135

MediumNEET2017

Preeti reached the metro station and found that the escalator was not working. She walked up the sationary escalator in time t1. On another days, if she remains stationary on the the moving escalator, then the escalator takes her up in time t2. The time taken by her to walk up on the moving escalator will be

Options:

A) {{{t_1}{t_2}} \over {{t_2} - {t_1}}}

B) {{{t_1}{t_2}} \over {{t_2} + {t_1}}}

C) {{t_1} - {t_2}}

D) {{{t_1} + {t_2}} \over 2}

136

MediumNEET2016

Two cars P and Q start from a point at the same time in a straight line and their positions are represented by xP(t) = (at + bt2) and xQ(t) = (ft $-$ t2). At what time do the cars have the same velocity ?

Options:

A) {{a - f} \over {1 + b}}

B) {{a + f} \over {2\left( {b - 1} \right)}}

C) {{a + f} \over {2\left( {1 + b} \right)}}

D) {{f - a} \over {2\left( {1 + b} \right)}}

137

MediumNEET2016

If the velocity of a particle is v = At + Bt2, where A and B are constants, then the distance travelled by it between 1 s and 2 s is

Options:

A) {3 \over 2}A + {7 \over 3}B

B) {A \over 2} + {B \over 3}

C) {3 \over 2}A + 4B

D) 3A + 7B

138

MediumNEET2015

A particle of unit mass undergoes one-dimensional motion such that its velocity varies according to $v\left( x \right) = \beta {x^{ - 2n}}, where \beta $ and n are constants and x is the position of the particle. The acceleration of the particle as a function of x, is given by

Options:

A) - 2{\beta ^2}{x^{ - 2n + 1}}

B) - 2n{\beta ^2}{e^{ - 4n + 1}}

C) - 2n{\beta ^2}{x^{ - 2n - 1}}

D) - 2n{\beta ^2}{x^{ - 4n - 1}}

139

MediumNEET2013

The displacement 'x' (in meter) of a particle of mass 'm' (in kg) moving in one dimension under the action of a force, is related to time 't' (in sec) by t = $\sqrt x + 3$. The displacement of the particle when its velocity is zero, will be

Options:

A) 4 m

B) 0 m (zero)

C) 6 m

D) 2 m

140

MediumNEET2013

A stone falls freely under gravity. It covers distances h1, h2 and h3 in the first 5 seconds, the next 5 seconds and the next 5 seconds respectively. The relation between h1, h2 and h3 is

Options:

A) h2 = 3h1 and h3 = 3h2

B) h1 = h2 = h3

C) h1 = 2h2 = 3h3

D) {h_1} = {{{h_2}} \over 3} = {{{h_3}} \over 5}

141

MediumNEET2012

The motion of a particle along a straight line is described by equation x = 8 + 12t $-$ t3 where x is in metre and t in second. The retardation of the particle when its velocity becomes zero is

Options:

A) 24 m s$-$2

B) zero

C) 6 m s$-$2

D) 12 m s$-$2

142

MediumNEET2011

A particle covers half of its total distance with speed v1 and the rest half distance with speed v2. Its average speed during the complete journey is

Options:

A) {{{v_1} + {v_2}} \over 2}

B) {{{v_1}{v_2}} \over {{v_1} + {v_2}}}

C) {{2{v_1}{v_2}} \over {{v_1} + {v_2}}}

D) {{v_1^2v_2^2} \over {v_1^2 + v_2^2}}

143

MediumNEET2011

A boy standing at the top of a tower of 20 m height drops a stone. Assuming g = 10 m s$-$2, the velocity with which it hits the ground is

Options:

A) 10.0 m/s

B) 20.0 m/s

C) 40.0 m/s

D) 5.0 m/s

144

MediumNEET2010

A particle moves a distance x in time t according to equation x = (t + 5)$-$1. The acceleration of particle is proportional to

Options:

A) (velocity)3/2

B) (distance)2

C) (distance)$-$2

D) (velocity)2/3

145

MediumNEET2010

A ball is dropped from a high rise platform at t = 0 starting from rest. After 6 seconds another ball is thrown downwards from the same platform with a speed v. The two balls meet at t = 18 s. What is the value of v? (Take g = 10 m/s2)

Options:

A) 75 m/s

B) 55 m/s

C) 40 m/s

D) 60 m/s

146

MediumNEET2009

A bus is moving with a speed of 10 ms$-$1 on a straight road. A scooterist wishes to overtake the bus in 100 s. If the bus is at a distance of 1 km from the scooterist, with what speed should the scooterist chase the bus ?

Options:

A) 40 m s$-$1

B) 25 m s$-$1

C) 10 m s$-$1

D) 20 m s$-$1

147

MediumNEET2009

A particle starts its motion from rest under the action of a constant force. If the distance covered in first 10 seconds is S1 and that covered in the first 20 seconds is S2, then

Options:

A) S2 = 3S1

B) S2 = 4S1

C) S2 = S1

D) S2 = 2S1

148

MediumNEET2008

A particle moves in a straight line with a constant acceleration. It changes its velocity from 10 ms$-1 to 20 ms-$1 while passing through a distance 135 m in t second. The value of t is

Options:

A) 12

B) 9

C) 10

D) 1.8

149

MediumNEET2008

The distance travelled by a particle starting from rest and moving with an acceleration ${4 \over 3}m s-$2, in the third second is

Options:

A) {{10} \over 3}$ m

B) {{19} \over 3}$ m

C) 6 m

D) 4 m

150

MediumNEET2007

A particle moving along x-axis has acceleration f, at time t, given by f = f0$\left( {1 - {t \over T}} \right),$ where f0 and T are constants.The particle at t = 0 has zero velocity. In the time interval between t = 0 and the instant when f = 0, the particle's velocity (vx) is

Options:

A) {1 \over 2}$ f0T2

B) f0T2

C) {1 \over 2}$ f0T

D) f0T

151

MediumNEET2007

A car moves from X to Y with a uniform speed vu and returns to Y with a uniform speed vd. The average speed for this round trip is

Options:

A) \sqrt {{v_u}{v_d}}

B) {{{v_d}{v_u}} \over {{v_d} + {v_u}}}

C) {{{v_u} + {v_d}} \over 2}

D) {{2{v_d}{v_u}} \over {{v_d} + {v_u}}}

152

MediumNEET2007

The positions x of a particle with respect to time t along x-axis is given by x = 9t2 $-$ t3 where x is in metres and t in seconds. What will be the position of this particle when it achieves maximum speed along the + x direction ?

Options:

A) 54 m

B) 81 m

C) 24 m

D) 32 m

153

MediumNEET2006

A particle moves along a straight line OX. At a time t (in seconds) the distance x (in metres) of the particle from O is given by x = 40 + 12t $-$ t3. How long would the particle travel before coming to rest ?

Options:

A) 16 m

B) 24 m

C) 40 m

D) 56 m

154

MediumNEET2006

A car runs at a constant speed on a circular track of radius 100 m, taking 62.8 seconds for every circular lap. The average velocity and average speed for each circular lap respectively is

Options:

A) 10 m/s, 0

B) 0, 0

C) 0, 10 m/s

D) 10 m/s, 10 m/s.

155

MediumNEET2006

Two bodies A (of mass 1 kg) and B (of mass 3 kg) are dropped from heights of 16 m and 25 m, respectively. The ratio of the time taken by them to reach the ground is

Options:

A) 4/5

B) 5/4

C) 12/5

D) 5/12

156

MediumNEET2005

The displacement x of a particle varies with time t as x = ae$-at + be\beta t, where a, b, \alpha and \beta $ are positive constants. The velocity of the particle will

Options:

A) be independent of $\beta

B) drop to zero when $\alpha = \beta

C) go on decreasing with time

D) go on increasing with time.

157

MediumNEET2005

A ball is thrown vertically upward. It has a speed of 10 m/sec when it has reached one half of its maximum height. How high does the ball rise? (Take g = 10 m/s2.)

Options:

A) 10 m

B) 5 m

C) 15 m

D) 20 m

158

MediumNEET2003

If a ball is thrown vertically upwards with speed u, the distance covered during the last t seconds of its ascent is

Options:

A) ut

B) {1 \over 2}$ gt2

C) ut $- {1 \over 2}$ gt2

D) (u + gt) t.

159

MediumNEET2003

A man throws balls with the same speed vertically upwards one after the other at an interval of 2 seconds. What should be the speed of the throw so that more than two balls are in the sky at any time ? (Given g = 9.8 m/s2)

Options:

A) more than 19.6 m/s

B) at least 9.8 m/s

C) any speed less than 19.6 m/s

D) only with speed 19.6 m/s.

160

MediumNEET2001

A particle is thrown vertically upward. Its velocity at half of the height is 10 m/s, then the maximum height attained by it (g = 10 m/s2)

Options:

A) 8 m

B) 20 m

C) 10 m

D) 16 m

161

MediumNEET2000

Motion of a particle is given by equation s = (3t3 + 7t2 + 14t + 8) m. The value of acceleration of the particle at t = 1 sec is

Options:

A) 10 m/s2

B) 32 m/s2

C) 23 m/s2

D) 16 m/s2

161

Total Questions

Easy

113

Medium

Hard

Study Tips

Before You Start

• Review the chapter concepts thoroughly
• Keep a notebook for important formulas
• Practice similar problems from your textbook
• Time yourself to improve speed

After Practice

• Review all incorrect answers carefully
• Watch video solutions for difficult questions
• Make notes of common mistakes
• Practice similar questions again later