Finding position and velocity from Force (analytic mechanics)

  • #1

Homework Statement

A body of mass "m" is repelled from the origin by a force F(x). The body is at rest at x_0, a distance from the origin, at t=0. Find v(x) and x(t).

Homework Equations


The Attempt at a Solution

I first perform the following steps:


The next step is to integrate v(x) WRT time. Doing this will solve for the position. My homework states that x(t) should be:


If I integrate v(x) WRT time, I will get a different answer for position than the equation above. Is my expression for v(x) incorrect?

Answers and Replies

  • #2
You should integrate v(t) over time and not v(x).
As you don't have v(t) you can instead write
dx/dt=v(x) , separate the variables and integrate both sides.
I mean, integrate
dx/v(x)= dt

You'll get t = some function of x. Then solve for x and you'll get x(t).

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