# Finding force and equation of motion

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1. Dec 6, 2014

### Jared Hill

1. The problem statement, all variables and given/known data
If v(x)=ax-2, then what is its force in terms of x. What is its motion as a function of time when x=a?

2. Relevant equations

3. The attempt at a solution

2. Dec 6, 2014

### ehild

What is v(x)? The motion of what are you speaking about?
Show the relevant equations and your attempt to solve the problem.

3. Dec 6, 2014

### Jared Hill

It is the motion along a horizontal frictionless plane. I did F=m dv/dt= m dv/dx*dx/dt= -2ma2x-5
Then I fould potential energy by integration. However I could not find the motion of the particle.

4. Dec 6, 2014

### ehild

How do you specify the motion of a particle at a given time or at a given place? You give the velocity and acceleration. What are they at x=a?

5. Dec 6, 2014

### Jared Hill

Sorry for the incomplete question.
If the particle starts at the position x = a, find its motion as a function of time.

6. Dec 7, 2014

### ehild

You know that v=dx/dt. You have the equation dx/dt=ax-2 This is a very simple separable differential equation. Can you solve?