At 2:00 PM a car's speedometer reads 30 mi/h. At 2:10 PM it reads 50 mi/h. Show that at some time between 2:00 and 2:10 the acceleration is exactly 120 mi/h^2.

Answer 1

The average acceleration is (50-30)/(1/6) = 120

Since velocity is continuous, the mean value theorem guarantees that the stipulated condition exists. Maybe everywhere, but surely somewhere.