Linear Speed of a Truck. Each tire on a truck has a radius of 16 inches. The tires are rotating at 440 revolutions per minute. Find the speed of the truck to the nearest mile per hour.
A)13 mph
B)31 mph
C)21 mph
D)80 mph
E)42 mph

Question

Quizplus · Accepted Answer

The linear speed $v$ of the truck can be found using the formula $v = 2\pi r \times \text{RPM}$, where $r$ is the radius of the tire and \text{RPM} is the revolutions per minute. First, convert the radius from inches to miles ($16 \text{ inches} = \frac{16}{63360} \text{ miles}$, since there are 63,360 inches in a mile) and the RPM to revolutions per hour ($440 \times 60$). Then, calculate the linear speed and convert it to miles per hour. The calculation is as follows:$$v = 2\pi \times \frac{16}{63360} \times (440 \times 60)$$$$v \approx 42 \text{ mph}$$Therefore, the speed of the truck is approximately 42 mph.