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A moving train is brought to rest within ` 20` seconds by applying brakes. Find the initial velocity , if the retardation due to brakes is `2 m//s^(2)`.

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In this problem we have been given the value of retardation but we require the value of acceleration. We know that retardation is negative acceleration. So, if the retardation is, `+2m s^(-2)` (as given here), then the acceleration will be, `-2 ms^(-2)` (the minus sign here indicate the negative acceleration). Let us solve the problem now.
Here, Initial velocity, `u` = ? (To be calculated) ltBrgt Final velocity, `v` = 0 (The train stops)
Acceleration, `a` = `-2ms^(-2)`
And, `" "` Time, `t` = 20 s
Now, putting these value in the formula :
`" "v=u+at`
We get : `" "0 =u+(-2) xx 20`
`" "0=u-40` ltBrgt `" "u=40ms^(-1)`
Thus, the initial velocity of the train is 40 metres per second.

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