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A particle having a velocity v = v(0) " ...

A particle having a velocity `v = v_(0) " at " t = 0` is accelerated at a rate `|a| = alpha sqrtv`, where `alpha` is a positive constant. Calculate the distance travelled before the particle is brought to rest.

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The correct Answer is:
`S = (2)/(3) (v_(0)^(1//2))/(alpha)`
`a = v (dv)/(dS) = alpha sqrtv`
`int_(v_(0))^(0) sqrtv dv = int_(0)^(S) alpha dS`
`S = (2)/(3) (v_(0)^(1//2))/(alpha)`
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