Question

Between two stations a train starting from rest first accelerates uniformly, then moves with constant velocity and finally retarts uniformly to come to rest. If the ratio of the time taken be `1 : 8 : 1` and the maximum speed attained be `60 km//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

Correct Answer - C
Given `u = 0`. Let during three phases time taken are t, `8t` and t respectively. `v_(max) = at = 60 km//h`
`v_(av) = ((1)/(2) at^2 + v_(max) 8t + (1)/(2)at^2)/(t + 8t + t)`
=`( at^2 + 8v_(max) t)/(10 t)=(at + 8v_(max))/(10)`
=`(60 + 8 xx 60)/(10) = 54 km//h`.