Siddharth M. answered • 09/03/24
Experienced Math, Physics and Electrical Engineering Tutor
To find the linear speed of the truck in mph, we can use the relationship between the rotational speed of the wheels and their linear speed.
Determine the circumference of the wheel: The circumference C of the wheel is given by: C = π × d,
where d is the diameter of the wheel.
Given d = 34 inches, we have:
C = π×34 ≈ 106.81 inches.
Find the linear speed in inches per minute: The linear speed v of the truck is the distance the truck travels in one minute. It is given by:
v=circumference × revolutions per minute
So, v=106.81 × 450 ≈ 48064.5 inches per minute.
Convert inches per minute to miles per hour: To convert the speed to mph, we need to convert inches per minute to miles per hour.
- There are 12 inches in a foot, and 5280 feet in a mile, so there are 12 × 5280 = 63360 inches in a mile.
- There are 60 minutes in an hour.
Therefore,
Speed in mph = (48064.5 inches per minute / 63360 inches per mile) × 60 minutes per hour
Speed in mph ≈ (48064.5 / 63360) × 60 ≈ 45.51 mph
So, the linear speed of the truck is approximately 45.51 mph.
