Finding velocity from force function F(x) = A + Bx

[jumbogala]

Homework Statement

The function given to me is F(x) = A + Bx.

x is the displacement, F(x) is the force as a function of that displacement, and A and B are constants.

From the function, I'm supposed to find the velocity of the function as a function of x.

We also know that the items which follow this function have mass m.

Homework Equations

The Attempt at a Solution

First I tried using F = ma, giving ma = A + Bx. Then I divided by m on both sides to get a = A/m + (B/m)x.

Then I integrated both sides, to get v = whatever the integral of the RHS is.

But then I realized that a = dv/dt, NOT dv/dx. So integrating with respect to dt doesn't work.

So instead I think I should use a = dv/dt = (dx/dt)*(dv/dx) = v(dv/dx)

And work that into my equation somehow. But I'm having a mental debate with myself about whether I was right the first time... can anyone help?

 

[rl.bhat]

You are right. Proceed.

 

[jumbogala]

So my 2nd reasoning is correct, not my first, right?

If I do that it works fine, it's just a simple integration. Thanks!