Question

Btw 2 stations a train accelerates uniformly at first then moves with constant speed and finally retards uniformly. If the ratios of time taken are 1:8:1 and the greatest spewd is 60km/h, find the average speed over the whole journey

Answer 1

The following velocity-time graph results

now, the total distance travelled will be given by the area under the vt curve. Now, as the geometry is trapezoidal in shape
area = (1/2)[a + b] x h
s = (1/2)[8t + 10t] x 60
or
s = 540t
now, the average speed will be
vav = total distance travelled / total time taken
= 540t / 10t
thus,
Vav = 54 km/hr