Question

At 9:13AM a car is traveling at 35 miles per hour. Two minutes later, the car istraveling at 85 miles per hour. Prove that are some time during this two-minuteinterval, the car’s acceleration is exactly 1500 miles per hour squared. Compute the value of A.

Answer 1

Answer:

There is at least one instant which instantaneous acceleration is equal to average acceleration. $a = 1500\,\frac{km}{h^{2}}$.

Explanation:

The average acceleration experimented by the car is:

$\bar a = \frac{85\,\frac{km}{h} - 35\,\frac{km}{h} }{\frac{2}{60}\,h }$

$\bar a = 1500\,\frac{km}{h^{2}}$

According to the Rolle's Theorem, there is at least one instant t so that instantaneous acceleration equal to average acceleration for the analyzed interval. That is to say:

$v'(c) = \frac{v(\frac{2}{60} )-v(0)}{\frac{2}{60}-0}$

If car is accelerating at constant rate, instantaneous acceleration coincides with average acceleration for all instant t. Then, instantaneous acceleration is:

$a = 1500\,\frac{km}{h^{2}}$