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In this video you will learn how to find the Rate of Change of the Distance between the two cars as they approach the same intersection, given their individual speed and distance from the intersection at time t.

A car is travelling at 50 miles per hour due south at a point 1/2 mile north of an intersection. A police car is travelling at 40 miles per hour due west at a point 1/4 mile east of the same intersection. At that instant, the radar in the police car measures the rate at which the distance between the two cars is changing. What does the radar gun register?

0:34 Drawing & Understanding picture with given Info

2:43 Understanding the third Variable needed to be found

4:08 Labeling given Distances of the two cars from the intersection

4:50 Using the Pythagorean Theorem to relate all variables - finding equation involving the third Variable d(t)

5:27 Differentiating the found equation implicitly

7:02 Plugging known quantities into the resulting equation - finding what to solve for - d'(t)

11:26 Solving for d'(t)

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