Question

Two trains $\text{A}$ and $\text{B}$ have lengths $800\text{m}$ and $1000\text{m}$ respectively and are moving with the velocity of $25\text{m/s}$ and $15\text{m/s}$ respectively in the same direction. At time $t=0$ engine of train $\text{A}$ is just behind train $\text{B}$. Find time when train $\text{A}$ completely overtakes train $\text{B}$?

• A. $10\text{sec}$
• B. $36\text{sec}$
• C. $18\text{sec}$
• D. $180\text{sec}$

Answer 1

The correct option is D $180\text{sec}$

At time $(t=0)$, let head of train $\text{A}$ is just behind the tail of train $\text{B}$.


At time $t=t_0$ let the head of train $\text{B}$ is just behind the tail of train $\text{A}$.


From, the two situations we see that in time $t_0$ relative displacement of train $\text{A}$ with train $\text{B}$ is
${\overrightarrow{S}}_{AB}=800+1000=+1800\text{m}$

Relative velocity of train $\text{A}$ w.r.t train $\text{B}$

$\overrightarrow{V_{AB}}=\overrightarrow{V_A}-\overrightarrow{V_B}=+25-(+15)$

$\Rightarrow {\overrightarrow{V}}_{AB}=+10\text{m/s}$

As the relative acceleration is zero. So,

Time taken $t_0=\frac{{\overrightarrow{S}}_{AB}}{{\overrightarrow{V}}_{AB}}=\frac{1800}{10}$

$\therefore t_0=180\text{seconds}$.

Hence, option (d) is the correct answer.

Key Concept:When relative acceleration is zero then, $\text{Relative velocity}=\frac{\text{Relative displacement}}{\text{time taken}}$