최대 1 분 소요

# Questions

## Question 1

At 2:00 p.m. a car’s speedometer reads 50$km/h$. At 2:20 p.m. it reads 65$km/h$. Show that at some time between 2:00 and 2:20 the acceleration is exactly 45$km/h^{2}$.

Let $v(t)$ be the velocity of the car $t$ hours after 2:00 p.m. Then $\frac{v(1/3) - v(0)}{1/3 - 0} = ?$. By the Mean Value Theorem, there is a number $c$ such that $0 < c < ?$ with $v^{'}(c) = ?$. Since $v^{'}(t)$ is the acceleration at time $t$, the acceleration $c$ hours after 2:00 p.m. is exactly 45 $km/h^{2}$.