An auto race is held on a circular track. A car completes one lap in a time of 19.2 s, with an average tangential speed of 39.8 m/s
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Oops!! Find the following......
(a) the average angular speed
(b) the radius of the track
(a) is 2pi / 19.2s = .327 rad/s
(b) .......
(b) radius=tangential speed/angular speed.
39.8/.327=121.7m
To calculate the circumference of the circular track, we can use the formula:
C = 2πr
where C is the circumference and r is the radius of the track.
The average tangential speed of the car is given as 39.8 m/s. Tangential speed is the speed of an object moving in a circular path at a given point, which is equal to the derivative of its displacement with respect to time. In this case, the tangential speed is the same as the average speed of the car throughout the lap.
The time taken to complete one lap is given as 19.2 s.
Using the formula for average speed:
Average speed = total distance / total time
We can rearrange the formula to solve for the total distance:
Total distance = average speed × total time
Substituting the given values:
Total distance = 39.8 m/s × 19.2 s = 763.2 m
Since the total distance is equal to the circumference of the circular track, we can substitute this value into the formula for the circumference:
763.2 m = 2πr
Simplifying the equation:
r = 763.2 m / (2π) ≈ 121.35 m
Therefore, the radius of the circular track is approximately 121.35 meters.