Question

An athlete doing agility training starts at A and runs to point B and then turns and runs back to point A and turns again and runs back to point B. The position for the athlete at time t is given by s(t)=t³-9t-2. On which intervals is the velocity negative? In which direction is the athlete running during these times interval?

Answer 1

When moving from B to A, the athlete's speed will be negative.

$$v(t)=s'(t)=3t^2-9$$

$$a(t)=s''(t)=6t$$

$$3t^2-9<0$$

$$(t-\sqrt 3)(t+\sqrt 3)<0$$

$$(0,\sqrt 3)$$

At this time, the speed is negative.