The acceleration (a) of a particle moving in a straight line varies with its displacement (s) as `a=2s+1`. The velocity of the particle is zero at zero displacement. Find the corresponding velocity-displacement equation.

Explanation

` a = 2s +1 rArr (dv)/(dt) = 2s +1 rArr (dv)/(ds) * ( ds)/(dt) = 2s +1 rArr (dv)/(ds)*v= 2s+1`
`" " rArr oversetv underset0 int v dv = 2 oversets underset0 int s ds + oversets underset 0 int ds `
`" " rArr ((v^(2))/(2))_(0)^(v) = 2((s^(2))/(2))_0^(s) + [s]_(0)^(s)" " rArr (v^(2)) /(2)= s^(2)+ s rArr v = sqrt(2s(s+1))`