A person is to run a circular track with a radius of 93 meters. The person starts at a certain spot and runs 3 and 1/2 times around the track in a time of 227 seconds. Find the magnitude of average velocity for this trip (|vav|) and find the average speed for this trip. Then subtract the magnitude of the average velocity from the average speed (avg. speed - |vav|). Answer in m/s.
To find the magnitude of average velocity for this trip, we need to determine the distance covered and the time taken.
The distance covered is equal to the circumference of the circular track, which can be calculated using the formula: circumference = 2πr.
Given that the radius of the track is 93 meters, we can calculate the circumference as follows:
circumference = 2 * π * 93 ≈ 584.5 meters.
Next, we need to determine the time taken to run 3 and 1/2 times around the track. Since the person completes the entire track 3 and 1/2 times, we can multiply the circumference by 3.5. The time taken is 227 seconds.
Now we can calculate the magnitude of average velocity:
average velocity = total distance / total time.
average velocity = (circumference * 3.5) / 227.
Substituting the values, we get:
average velocity = (584.5 * 3.5) / 227 ≈ 8.97 m/s (rounded to two decimal places).
To determine the average speed for this trip, we need to find the total distance covered and divide it by the total time taken.
The total distance covered can be found by multiplying the circumference by 3.5:
total distance = circumference * 3.5 = 584.5 * 3.5 = 2045.75 meters.
The average speed is given by:
average speed = total distance / total time.
average speed = 2045.75 / 227 ≈ 9.01 m/s (rounded to two decimal places).
Finally, to find the difference between the magnitude of the average velocity and the average speed, subtract the magnitude of the average velocity from the average speed:
average speed - magnitude of average velocity = 9.01 - 8.97 ≈ 0.04 m/s.
Therefore, the difference between the magnitude of the average velocity and the average speed is approximately 0.04 m/s.