Using Derivatives and Integrals to Find Velocity: Am I doing this right?

  • Thread starter jumbogala
  • Start date
  • #1
423
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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 in to my equation somehow. But I'm having a mental debate with myself about whether I was right the first time... can anyone help?
 

Answers and Replies

  • #2
rl.bhat
Homework Helper
4,433
7
You are right. Proceed.
 
  • #3
423
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So my 2nd reasoning is correct, not my first, right?

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

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