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A particle starts from rest and moves wi...

A particle starts from rest and moves with an acceleration of `a={2+|t-2|}m//s^(2)` The velocity of the particle at `t=4` sec is

Text Solution

Verified by Experts

Acceleration can be written as,
`a = 2 + 2 - t = 4 - t` for `t le 2 s`.
and `a = 2 + t - 2 = t` for `t ge 2 s`.
Therefore, acceleration -time graph of the particle will be as in figure.
Now since, `underset(v_(1))overset(v_(f))int dv = int a dt`
`rArr v_(f) - v_(i) =` area under `a - t` graph
or `v_(f) - 0 = 4 xx 4 - (1)/(2) xx 4 xx 2 = 12 m//s`
i.e., velocity of particle at the end of 4 s is `12 m//s`
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