Question

The distance between your car's front wheels is 4.08 meters. You drive around a racetrack, counterclockwise, one complete circle every 21.67 second. The driver side front wheel has an average speed of 24.0 m/s, what is passenger side front wheel's average speed? (Hint: one may assume it's a circular racetrack and first find its radius, although the answer should be the same for any shape of racetrack)

Answer 1

The average speed of the passenger side front wheel is 24.0 m/s, the same as the driver side front wheel, since both wheels complete their respective circles in the same period of time on a circular track.

Step-by-step explanation:

To find the average speed of the passenger side front wheel of a car traveling around a circular racetrack, first, we need to determine the radius of the racetrack based on the given speed of the driver side front wheel and the time it takes to complete a circuit. The speed (v) of the driver side wheel is given as 24.0 m/s, and the time (T) to complete a circle is 21.67 seconds. Using the formula for the circumference of a circle (C = 2πr) and the fact that speed equals distance over time (v = d/T), we can find the radius (r).

C = v × T
r = C / (2π)

Given that the car's wheels are 4.08 meters apart, and it moves counterclockwise, the distance each wheel travels will differ. The passenger side wheel travels a circle with a radius = r + 4.08/2 meters. Since speed is given by distance over time, and the time remains the same for both wheels, we determine the circumference of the circle the passenger side wheel travels, and thus ideally, the average speed remains the same for the passenger side front wheel as for the driver side wheel (24.0 m/s) if the car is driving around a circular track. This is due to the fact that both wheels complete their respective circles in the same period (21.67 seconds).