Question

A passenger train is moving at $5m{s}^{-1}$ . An express train is travelling at $30m{s}^{-1}$, on the same track and rear side of the passenger train at some distance. The driver in express train applied brakes to avoid collision. If the retardation due to brakes is $4m{s}^{-2}$, the time in which the accident is avoided after the application of brakes is

• A. $4.25$
• B. $5.25$
• C. $6.25$
• D. $7.25$

Answer 1

The correct option is C

$6.25$

Step 1. Given Data:

Speed of passenger train, $U_p=5m{s}^{-1}$

Speed of express train, $U_e=30m{s}^{-1}$

Retardation due to brakes, $a=4m{s}^{-2}$

Step 2. The initial relative velocity of the express train with respect to the passenger train:

$$\begin{gathered} U=U_e-U_p \\ \Rightarrow U=30-5 \\ \Rightarrow U=25m{s}^{-1} \end{gathered}$$

The final relative velocity of the express train with respect to the passenger train, $V=0$ ( Because express train comes to rest relative to the passenger train )

Step 3. From the first equation of motion:

$$\begin{gathered} V=U-at \\ \Rightarrow 0=25-4t \\ \Rightarrow 4t=25 \\ \Rightarrow t=6.25s \end{gathered}$$

Hence, the correct option is (C).