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Question
A train starts from rest and moves with a constant acceleration of 2.0 m/s2 for half a minute. The brakes are then applied and the train comes to rest in one minute. Find the position(s) of the train at half the maximum speed.
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Solution
Initial velocity, u = 0
Acceleration, a = 2 m/s2
Let the final velocity be v before the brakes are applied.
Now,
t = 30 s
v = u + at
v = 0 + 2 × 30
⇒ v = 60 m/s
Half the maximum speed \[= \frac{60}{2} = 30 \text{ m } /s\]
When the train is accelerating with an acceleration of 2 m/s2:
Distance,
When the train is decelerating with an acceleration of - 1 m/s2:
Distance,
Position from the starting point = 900 + 1350 = 2250
= 2.25 km
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