Question

Between two stations a train starting from rest first accelerates uniformly, then moves with constant velocity and finally retards uniformly to come to rest. If the ratio of the time taken be $1:8:1$ and the maximum speed attained be $60km/h$, then what is the average speed over the whole journey?

• A. 48 km/h
• B. 52 km/h
• C. 54 km/h
• D. 56 km/h

Answer 1

Answer: (C)

Given $u=0$. Let during three phases time taken are $t$,

$8t$ and $t$ respectively. $v_{max}=at=60km/h$

$v_{av}=\frac{\frac{1}{2}a{t}^2+v_{max}8t+\frac{1}{2}a{t}^2}{t+8t+t}$

$=\frac{a{t}^2+8v_{max}t}{10t}=\frac{at+8v_{max}}{10}$

$=\frac{60+8\times 60}{10}=54km/h$