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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 23/2ms-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,

mvdv/dx=3x+6, so v2=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=ò0 Tdt=ò0 20dx/(sqrt(2)(x+2))

and just evaluate the integral.

Kerwin