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A train starts from rest and accelerates...

A train starts from rest and accelerates uniformly at a rate of `2 m s^(-2)` for 10 s. It then maintains a constant speed for 200 s. The brakes are then applied and the train is uniformly retarded and it comes to rest in 50 s. Find
(i) the maximum velocity reached,
(ii) the retardation in the last 50 s,
(iii) the total distance travelled, and
(iv) the average velocity of the train.

Text Solution

Verified by Experts

Lets, `s_1, s_2` and `s_3` be the distances travelled in the three stages.
(i) `v = u + at = 20 m s^(-1)`
(ii) `v = u + at`
`therefore a = - 0.4 m s^(-2)`
(iii) `s_1 = 1/2 at^2 = 1/2 xx 2 xx 100 = m`
`s_2 = 4000 m,s_3 = 500 m`
Total s. = 4600 m
(iv) `17.69 ms^(-1)`
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