Question

A ball rolling down an incline travels s feet in t seconds, where s= 5t^2. Derive a formula for the velocity of the ball at time t= t0. How fast is it going (a) after 2 seconds (b) after it has rolled 80 feet?

Answer 1

$$v(t)=s'(t)=(5t^2)'=10t$$

$$v(t_0)=10t_0$$

(a) $t_1=2s$

$$v(t_1)=10(2)=20(ft/s)$$

(b)

$$s(t_2)=5t_2^2=80, t_2\ge0$$

$$t_2=\sqrt{16}=4(s)$$

$$v(t_2)=10(4)=40(ft/s)$$