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## Homework Statement

Show that d(v^2)/dt = 2 . (d^2r/dt^2) . (dr/dt)

HINT: v^2 = ||dr/dt||^2 = dr/dt . dr/dt

## Homework Equations

## The Attempt at a Solution

I did it another method:

d(v^2)/dt = d/dv(v^2) . dv/dt --------------chain rule

= 2v . dv/dt

since v=dr/dt and dv/dt = d^2r/dt^2

therefore = 2 . (d^2r/dt^2) . (dr/dt)

Is there a more rigorous method to solving this, using the 'HINT' it gave me. I can't quite figure it out.

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