A particle P of mass 1.5kg moves in a straight line through a fixed point O. At time ts after passing through O the distance of P from O is xm, and the force acting on P has magnitude (3x + 6) N directed away from O. Given that P passes through O with speed 2^3/2 ms^-1 , calculate the value of t when x = 20. Can anyone help? Thanks

mv dv/dx=3x+6, so v²=2(x+2)². Take the square root of both side and you get v=Ö2(x+2). Now recall that v=dx/dt, so we have

T=ò_o^T dt=ò₀²⁰ dx/(Ö2(x+2))

and just evaluate the integral.

Kerwin