a runner run halfway around a circular track whose radius is 60 meters in 45 secs
what is the average velocity?
what is the average speed?
4.19 m/s
To find the average velocity and average speed of the runner, we first need to determine the distance traveled by the runner. Given that the runner completes half a lap around a circular track with a radius of 60 meters, the distance traveled is equal to half of the circumference of the circle.
The formula to calculate the circumference of a circle is C = 2πr, where C represents the circumference and r is the radius. In this case, the radius is 60 meters, so the formula becomes:
C = 2π(60) = 120π meters
To find the distance traveled by the runner, we divide the circumference by 2:
Distance = (120π) / 2 = 60π meters
Now that we know the distance, we can calculate the average velocity and average speed.
Average velocity is defined as the change in position (displacement) divided by the time taken. In this case, the runner starts and ends at the same position, so the displacement is zero.
Average velocity = displacement / time = 0 / 45 = 0 meters per second
Therefore, the average velocity of the runner is 0 meters per second.
Average speed, on the other hand, is defined as the total distance traveled divided by the time taken. In this case, the total distance covered is 60π meters.
Average speed = distance / time = (60π) / 45 = (4π) / 3 meters per second
Therefore, the average speed of the runner is (4π) / 3 meters per second.