Suppose that you, law-abiding driver that you are, are going along the highway at the posted speed limit of 70 mph. You see in your rear-view mirror a car traveling at high speed in the lane next to yours. Suppose that car is traveling at 100 mph. At the instant that the other car is right next to you, you both see an obstruction ahead, say a tree lying across the road. You both slam on your brakes to the maximum and you come to rest just before you hit the barrier. What would be the speed with which the other car hits the tree?
Making some simple assumptions, such as that both cars and drivers are very similar, this problem becomes an elementary physics problem that anyone who knows basic kinematics can solve. Even if you don’t you can make a guess. The point of the problem is that the result was quite surprising, even for me. It would be a good problem to give introductory physics students, both as an application of physics and to alert them to the dangers of speeding.
This video gives the solution and different ways of arriving at it.
(Via Mark Frauenfelder.)