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.
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?