Newton's 2nd Law Question

By Carl Evans on Sunday, September 30, 2001 - 07:10 pm:

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

By Kerwin Hui on Sunday, September 30, 2001 - 07:23 pm:

Carl,

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

$T = \int_{o}^{T} dt = \int_{0}^{20} dx / (\sqrt{2} (x + 2))$

and just evaluate the integral.

Kerwin