A particle of mass m moves along a frictionless, horizontal plane with a speed given by v(x) = a/x, where x is its distance from the origin and a is a positive constant. Find the force F(x) to which the particle is subject.
The answer is -a^2/x^3.
Can anyone explain how that happened? This was my thought process when I solved it:
v(x) = a/x
a'(x) = will be the derivative = -a/x^2 = F(x)m
So the force F(x) = (-a^2*m)/x^2
Please explain in detail! All help is really appreciated.