Question

A train starts from rest from a station with acceleration $0.2m/s^2$ on a straight track and then comes to rest after attaining maximum speed on another station due to retardation $0.4m/s^2$. If total time spent is half an hour, then distance between two stations is [Neglect length of train]

• A. 216 km
• B. 512 km
• C. 728 km
• D. 1296 km

Answer 1

Answer: (A)

$S=\frac{1}{2}\frac{\alpha \beta }{\alpha +\beta }{T}^2$
$\alpha \to$ Acceleration
$\beta \to$ Deceleration (magnitude only)
$T\to$ Time of journey
$S\to$ Distance travelled
Given, $\alpha =0.2m{s}^{-2}$
$\beta =0.4m{s}^{-2}$
$T=$ half an hour $=30\times 60s=1800s$
$\Rightarrow S=\frac{1}{2}\times \left(\frac{0.2\times 0.4}{0.2+0.4}\right)\times (1800{)}^2$
$\Rightarrow S=216000m$
$\Rightarrow S=216km$