Finding force and equation of motion

AI Thread Summary
The discussion revolves around finding the force and equation of motion for a particle with the velocity function v(x) = ax - 2, specifically when x = a. Participants clarify that the motion occurs on a horizontal frictionless plane and attempt to derive the force using F = m dv/dt. The integration of force leads to potential energy, but the challenge remains in determining the motion of the particle over time. A suggestion is made to solve the separable differential equation dx/dt = ax - 2 to find the motion as a function of time. The conversation emphasizes the need to specify velocity and acceleration at the given position to fully describe the motion.
Jared Hill
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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

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

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