Question 8: Motion in 1D

Question

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 :

Accepted Answer

Average Velocity
$\langle \vec{v} angle$: Calculated using the formula
$   \langle \vec{v} angle = \frac{\Delta \overrightarrow{s}}{\Delta t} = \frac{S_f - S_i}{t_f - t_i}   $
where $S_f$ and $S_i$ are the final and initial displacements, respectively, and $t_f$ and $t_i$ are the final and initial times.
Instantaneous Velocity
$\overrightarrow{v}$: Given by the slope of the displacement vs. time graph at any specific time:
$   \overrightarrow{v} = \frac{ds}{dt} = 	ext{slope at that point}   $
Analysis of Each Time Interval:
(A) From $0$ to $3 \, 	ext{sec}$:
$ \langle \vec{v} angle = \frac{5 - 0}{3} = \frac{5}{3} \, 	ext{m/s} $
The statement that the average velocity is $10 \, 	ext{m/s}$ is incorrect based on our calculation.
(B) From $3$ to $5 \, 	ext{sec}$:
$ \langle \vec{v} angle = \frac{5 - 5}{2} = 0 \, 	ext{m/s} $
The average velocity is indeed $0 \, 	ext{m/s}$.
(C) At $t = 2 \, 	ext{sec}$:
The slope of the tangent line at $t = 2$ indicates that $\overrightarrow{v} = 5 \, 	ext{m/s}$. Therefore, this statement is correct.
(D) From $5$ to $7 \, 	ext{sec}$:
$ \langle \vec{v} angle = \frac{0 - 5}{2} = -2.5 \, 	ext{m/s} $
At $t = 6.5 \, 	ext{sec}$, the graph's slope shows that $\overrightarrow{v} = 10 \, 	ext{m/s}$, hence the statement is incorrect as the values are not equal.
(E) From $t = 0$ to $t = 9 \, 	ext{sec}$:
$ \langle \vec{v} angle = \frac{0 - 0}{9} = 0 \, 	ext{m/s} $
This statement is verified correct as the average velocity is zero over the entire period.
Based on the analysis, statements (B), (C), and (E) are correct.

Answer

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

Answer

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

Answer

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

Answer

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

Motion in 1D

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