The acceleration (a) of a particle moving in a straight line varies with its displacement (S) as `a=2S`. The velocity of the particle is zero and zero displacement. Find the corresponding velocity-displacement equation.

Explanation

`a=2Simpliesv(dv)/(ds)=2Simpliesvdv=2SdS`
`impliesint_(0)^(v)vdv=int_(0)^(s)2SdSimplies((v^(2))/(2))=2((S^(2))/(2))_(0)^(2)`
`implies(V^(2))/(2)=S^(2)impliesv+-sqrt(2S)`