6. A particle of mass m moves along a frictionless, horizontal plane with a speed given by
v(x) = α / x. Where x is the distance of the object from the origin and α is a constant.
Working with F = ma, we want to get the acceleration. You have v = v(x). You want a = dv/dt. Find (dv/dx)(dx/dt). Find the force F(x) to which the particle is subjected to.
The Attempt at a Solution
I guess my problem is I dont understand why I need to use chain rule since v = dx/dt. I thought I could take the derivative in respect to t on both sides, and get dv/dt = - α / x^2, then multiply both sides by m to get the force equation.
the answer is given, -m α^2/ x^3. So can someone explain what I'm missing here....