1. Tardigrade
  2. Question
  3. Physics
  4. 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 60 km/h, then what is the average speed over the whole journey?

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Q. 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 $60 \,km/h$, then what is the average speed over the whole journey?

Motion in a Straight Line

Solution:

Given $u = 0$. Let during three phases time taken are $t$,
$8t$ and $t$ respectively. $v_{max} = at = 60 \,km/h$
$v_{av} = \frac{\frac{1}{2} at^2 + v_{max} 8t + \frac{1}{2} at^2}{t + 8t + t}$
$ = \frac{at^2 + 8v_{max} t}{10 t} = \frac{at + 8v_{max}}{10}$
$ = \frac{60 + 8 \times 60}{10} = 54\,km/h$