Question
A force f[x] imparts an acceleration a[x] to an object of constant mass m moving (with no friction) along the x-axis from x = a
A force f[x] imparts an acceleration a[x] to an object of constant mass m moving (with no friction) along the x-axis from x = a to x = b.
Physicists have a notion of the work done by this force while it moves the object from x = a to x = b. They measure work with an integral:
Work = Integrate[m a[x], {x, a, b}].
Why is
a[x] = v[x]v'[x]
where v[x] is velocity at position x for a x b?
Tip - Remember that velocity is the derivative of position with respect to time, and acceleration is the derivative of velocity with respect to time. Use the chain rule:
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