Question

A train starts from rest and for the first kilometer moves with constant acceleration. For the next 3 kilometers it has constant velocity and for another two kilometers it moves with constant retardation to come to rest after a total time of 10 minutes. The maximum velocity of the train is

• A. 18 km / h
• B. 36 km / h
• C. 54 km / h
• D. 39 km / h

Answer 1

Answer: (C)

Let $v$ be the maximum velocity acquired by train while accelerating for time $t_1$, covering distance $1km$. Therefore,
$1=\left(\frac{0+v}{2}\right)t_1\text{ or }2=v{t}_1\dots (i)$
If $t_2$ is the time for uniform motion, then $3=v{t}_2\dots (ii)$
If $t_3$ is the time for retarded motion, then
$2=\left(\frac{v+0}{2}\right)\times t_3$ or $4=v{t}_3\dots (iii)$
Adding (i), (ii) and (iii), we get
$2+3+4=v\left(t_1+t_2+t_3\right)$
$=v\times \frac{10}{60}$ or $v=54km/h$