What is the acceleration?

Question

Suppose that the velocity of a falling body is v = ks ² (k a constant) at the instant the body has fallen s meters from its starting point. Find the body's acceleration as a function of s.

Answer 1

The body’s acceleration is the time derivative of v, dv/dt. By the chain rule, dv/dt = dv/ds * ds/dt. Note that dv/ds = 2ks and ds/dt = v = ks². Therefore, dv/dt = 2ks * ks² = 2k²s³.