Question

A metro train starts from rest and in 5 s achieves 108 km/h. After that it moves with constant velocity and comes to rest after travelling 45 m with uniform retardation. If total distance travelled is 395 m, find total time of travelling.

• A. 12.2 s
• B. 15.3 s
• C. 9 s
• D. 17.2 s

Answer 1

Answer: (D)

17.2 s

Initial velocity $=0m/s$

Initial acceleration, $a=\frac{(180\times \frac{1000}{3600})}{5}=6m/s^2$

Distance travelled in first 5 seconds:

$\Rightarrow s=\frac{1}{2}a{t}^2=\frac{1}{2}\times 6\times 25=75m$

Velocity after 5 seconds, $v=at=6\times 5=30m/s$

Train has moved 45m during retardation and came to rest.

$\Rightarrow v^2-u^2=2as\Rightarrow 0-(30\times 30)=(2\times a\times 45)\Rightarrow a=-10m/s^2$

Time taken to come to rest, $t=\frac{0-30}{-10}=3sec$

Distance travelled with uniform velocity $=395-(75+45)=275m$

Time taken to travel this distance $=\frac{275}{30}=9.2sec$

Total time $=9.2+3+5=17.2$ seconds

Hence, option D is correct.