1. Tardigrade
  2. Question
  3. Physics
  4. Between two stations, a train accelerates from rest uniformly at first, then moves with constant velocity, and finally retards uniformly to come to rest. If the ratio of the time taken is 1: 8: 1 and the maximum speed attained be 60 kmh -1, then what is the average speed over the whole journey?

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Q. Between two stations, a train accelerates from rest uniformly at first, then moves with constant velocity, and finally retards uniformly to come to rest. If the ratio of the time taken is $1: 8: 1$ and the maximum speed attained be $60\, kmh ^{-1}$, then what is the average speed over the whole journey?

Motion in a Straight Line

Solution:

$S_{1}=\frac{1}{2} a t^{2}=\frac{1}{2}(a t) t=\frac{60 t}{2}=30\, t$
$S_{2}=60 \times 8 t=480\, t, S_{3}=S_{1}=30\, t$
image
$v_{ av }=\frac{S_{1}+S_{2}+S_{3}}{t+8 t+t}$
$=54\, km h ^{-1}$