# Velocity as a function of distance problem

1. Jan 26, 2010

### Slepton

1. The problem statement, all variables and given/known data

The velocity of a ball of mass 'm' varies with the distance v(x) = ax-n, where a and n are positive constants.

Determine F(x), x(t) and F(t).

2. Relevant equations
F = ma
a = dv/dt
v = dx/dt

3. The attempt at a solution
If velocity were the function of time, i would have done it with no problem. I determined the acceleration, which is -nax-n-1.
For v, i integrated 'a' with respect to t. But velocity's dependence in distance confused me. Any help will be highly appreciated.
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

2. Jan 26, 2010

### aim1732

There is a simple way for these.
a=dv/dt. This can be written as a=dx/dt*dv/dx.

3. Jan 26, 2010

### rl.bhat

v = dx/dt = a*x^-n
So x^n*dx = a*dt.
Find the integration and then find x in terms of a, n and t.
Then d^2(x)/dt^2 will give acceleration in terms of a,n and t. from that you can find F(t)
Acceleration a = dv/dt = dv/dx*dx/dt = dv/dx*v. Then F(x) = ma

Last edited: Jan 26, 2010
4. Jan 26, 2010

To rl.bhat