1. ## Variable Applied Force

A particle 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 xcm and the force acting on P has magnitude (3x+6)N and is direced away from O. Given that P passes through the point O with speed 2(2^0.5)m/s, caculate:
a) the speed of P when x=5; thispart of the question I was able to do using intergration and obtained the correct answer of 9.90m/s.
b) the value of t when x=20. I don't know how to do this part of the question, though I assume calculus is needed once again. Can someone enlighten me please?

2. $F = ma$
$F = mv \frac{dv}{dx}$

find v in terms of x.

then you have something in the form of $dx/dt = f(x)$

allowing you to establish a relationship between displacement and time. Remember to evaluate your integration constants using the information given.

- Bobak