Question 108: Motion in 1D

Question

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 ________ $$m$$.

Accepted Answer

A bus traveling along a straight highway at a speed of 72 km/h comes to a stop within 4 seconds after the brakes are applied. To find the distance the bus travels during this time (assuming uniform deceleration), follow these steps:
First, convert the initial speed from km/h to m/s:
$$\begin{aligned} u &= 72 	imes \frac{5}{18} = 20 \, 	ext{m/s}  \end{aligned}$$
Given:
Initial speed ($ u $) = 20 m/s
Final speed ($ v $) = 0 m/s
Time ($ t $) = 4 s
Using the first equation of motion:
$$\begin{aligned} v &= u + at \ 0 &= 20 + 4a \ a &= -5 \, 	ext{m/s}^2  \end{aligned}$$
Now, use the second equation of motion to find the distance traveled ($ S $):
$$\begin{aligned} S &= ut + \frac{1}{2}at^2 \ S &= 20 	imes 4 + \frac{1}{2} 	imes (-5) 	imes 4^2 \ S &= 80 - 40 \ S &= 40 \, 	ext{m} \end{aligned}$$
Therefore, the distance traveled by the bus during the time the brakes are applied is 40 meters.

Motion in 1D

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

Integer / Numeric Answer Type