Reverse Physics and a Car

by Philip Newman

1. According to Newton's Law of Gravitation, all bodies are attracted to each other with a force inversly proportional to the square of the distance between them.

Can you find an example where the gravitational force decreases when two bodies are brought closer together?

2. A car, initially still, accelerates up to a maximum speed of v, and then slows down to a stop again. The plot of the velocity over the time (t seconds from start to stop) is a semicircle, shown in this diagram:

Now as all mathematicians know, it is often useful to find the area under the curve, in this case to find how far the car has travelled. One mathematician claims that since the radius of the semicircle is v, the distance travelled is (pi/2)*v^2. Another disagrees, saying that t is the diameter of the semicircle, so the distance is actually (pi/2)*(t/2)^2. Which one is right?

See the Solution