Answer to Question #77374 in Calculus for Vyea

Question

1) At 2.00 pm, a car’s speedometer reads 30 mi/h. At 2.10 pm it reads 50mi/h. Show that at some time between 2.00 pm and 2.10 pm the acceleration is exactly 120 mi/h²

2) Two runners start a race at the same time and finish in a tie. Prove that at some time during the race they have the same speed. [Hint: Consider f(t)=g(t)-h(t) ,where g and h are the position functions of the two runners.]