Question

A car travels down a highway at 25 m/s. An observer stands 150 m from the highway.

How fast is the distance from the observer to the car increasing when the car passes in front of the observer

Answer 1

Let x be the distance (in feet) along the road that the car has traveled and h be the distance (in feet) between the car and the observer.

(a) Before the car passes the observer, we have dh/dt < 0; after it passes, we have dh/dt > 0. So at the instant it passes the observer we have dh/dt = 0, given that dh/dt varies continuously since the car travels at a constant velocity.