Question

A compartment gets detached from a train, and comes to rest with a constant retardation. During this period, the train moves with a uniform velocity. Prove that the distance covered by the detached compartment and its distance from the train when it comes to rest, are equal to each other.

Answer 1

Dear Student,

Let t be the time of journey

Distance moved by train: S=ut..(i)

Now since the compartment wa in motion its initial velocity is u

So distance travelled by compartment,

$$\begin{gathered} S\text{'}=ut-\frac{1}{2}a{t}^2...\left(ii\right) \\ Dis\tan cebetweenthetrainandcompartmentafteritcametorest \\ S-S\text{'}=\frac{1}{2}a{t}^2 \\ orS\text{'}=S-\frac{1}{2}a{t}^{2}from\left(i\right)S\text{'}=ut-\frac{1}{2}a{t}^2 \end{gathered}$$
Regards.