Question

a thin uniform rod of length l cm and a small particle lie on a line separared by a distance of a cm. if K is a positive constant and F is measured in newtons, the gravitational force between them is F=K/(a(a +l))
a) if a is increasing at the rate 2cm/min when a=15 and l=5, how fast is F increasing?
b)if l is decreasing at the rate 2cm/min when a =15 and l=5, how fast is F increasing?

Answer 1

Use differentiation...
dF/dt = K(-1/a^2(a+l) - 1/(a+l)^2a)* da/dt , put in values
da/dt = 2cm/min
a=15
l=5

Answer 2

And, the force is decreasing in the first case as a is increasing