Finding force and equation of motion

[Jared Hill]

Homework Statement

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?

Homework Equations

The Attempt at a Solution

 

[ehild]

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

 

[Jared Hill]

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

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.

 

[ehild]

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.

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?

 

[Jared Hill]

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?

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

 

[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?