Between two stations a train accelerates uniformly at first, then moves with constant velocity and finally retards uniformly. If the ratio of the time taken for these is 1:8:1 and the maximum speed attained be 60 km h- then what is the average speed over the whole journey ?

Options

A. 48 `Kmh^(-1)`
B. 52`Kmh^(-1)`
C. 54`Kmh^(-1)`
D. 56`Kmh^(-1)`

Answer

c

Explanation

Here let `S_1, S_2,S_3` be the respectively distance moved in t,8t and t, then
`S_1=((60+0)/(2))t,S_2=60xx8t=480t`
and `S_3=((60+0)/(2))t=30t`
Then `v_("average")=(S_1+S_2+S_3)/(t+8t+t)`
`=(30t+480t+30t)/(10t)`
`=(540t)/(10t)`=54km/hour.