Question 13: Motion in 1D

Question

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 :

Accepted Answer

Let's analyze the given information before determining the distance between the two cars when they come to rest. Each car is traveling towards the other at a speed of $$20 \, 	ext{m s}^{-1}$$ and they both start braking when they are $$300 \, 	ext{m}$$ apart. The deceleration (negative acceleration) of each car is given as $$2 \, 	ext{m s}^{-2}.$$
To find the distance each car travels before coming to rest, we can use the kinematic equation that relates initial velocity ($$v_i$$), final velocity ($$v_f$$), acceleration ($$a$$), and distance ($$d$$), which is:
$$v_f^2 = v_i^2 + 2ad$$
Since the final velocity $$v_f = 0$$ (they come to rest), we can rearrange the equation to solve for $$d$$ (the distance each car travels before stopping):
$$0 = v_i^2 + 2ad \Rightarrow d = -\frac{v_i^2}{2a}$$
Plugging in the values for each car (noting that acceleration $$a$$ is negative because it is deceleration, so $$a = -2 \, 	ext{m s}^{-2}$$):
$$d = -\frac{(20)^2}{2(-2)} = -\frac{400}{-4} = 100 \, 	ext{m}$$
Each car travels $$100 \, 	ext{m}$$ before coming to rest. Since they both start $$300 \, 	ext{m}$$ apart and each travels $$100 \, 	ext{m}$$ towards the other, the total distance covered by both cars before stopping is $$2 	imes 100 \, 	ext{m} = 200 \, 	ext{m}$$.
To find the distance between them when they come to rest, we subtract the total distance covered by both cars from the original distance between them:
$$300 \, 	ext{m} - 200 \, 	ext{m} = 100 \, 	ext{m}$$
So, the distance between the cars when they come to rest is $$100 \, 	ext{m}$$. Therefore, the correct option is:
Option B
100 m

Answer

25 m

Answer

100 m

Answer

50 m

Answer

200 m

Motion in 1D

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 :

Choose the correct answer: