Question

For positive constants A and B, the force, F, between two atoms in a molecule at a distance r apart is given by
F = -\frac{A}{r^2} + \frac{B}{r^3}.


How fast does force change as r increases? (Your answer may involve A, B, and r.)

If at some time t the distance is changing at a rate k, at what rate is the force changing with time? (Your answer may involve A, B, r, and k.)
So I got the first part which is (2A/r^3)-(3B/r^4) but I'm not sure how to add the k in

Answer 1

\[F = -\frac{A}{r^2} + \frac{B}{r^3}\]
\[\frac{dF}{dr} = \frac{2A}{r^3} -\frac{3B}{r^4}\]
\[\frac{dr}{dt} = k\]
\[\frac{dF}{dt} = ?\]

Answer 2

THANKS!!!

Answer 3

What's your answer?

Answer 4

dF/dr*dr/dt=dF/dt
(2A/r^3-3B/r^4)*k

Answer 5

Great!