An athlete starts at point and runs at a constant speed of 5.40 around a round track 250 in diameter
Find the component of this runner's average velocity between points A and B.
Find the component of this runner's average velocity between points A and B.
Find the component of this runner's average acceleration between points A and B.
Find the component of this runner's average acceleration between points A and B.
For a problem such as this, a figure must be provided. The answer depends upon where A and B are on the circle. The dimensions of the speed and diameter must also be provided, not just a number.
To find the component of the runner's average velocity and acceleration between points A and B on a circular track, we need to know the specific locations of A and B on the track as well as the dimensions of the track and the speed of the athlete. For example, if we assume that point A is at the top of the track and point B is at the bottom, we can provide a solution.
Let's assume that the track is a circle with a diameter of 250 meters and the athlete is running at a constant speed of 5.40 m/s.
1. Component of average velocity:
To find the component of the average velocity between points A and B, we need to calculate the displacement of the runner. Since the runner starts at point A and finishes at point B, the displacement is equal to the circumference of half the track (from A to B), which is half the circumference of the entire track.
Circumference of the track = π * diameter = π * 250 m ≈ 785.4 m
Displacement from A to B = 0.5 * 785.4 m = 392.7 m
The time taken to complete this displacement will depend on the speed of the runner. The average velocity is the displacement divided by the time taken.
Average velocity = Displacement / Time taken
To calculate the time taken, we divide the displacement by the runner's speed:
Time taken = Displacement / Speed = 392.7 m / 5.40 m/s ≈ 72.6 s
Therefore, the component of the runner's average velocity between points A and B is equal to the displacement divided by the time taken:
Component of average velocity = Displacement / Time taken = 392.7 m / 72.6 s ≈ 5.41 m/s
2. Component of average acceleration:
To calculate the component of the average acceleration, we need to know the initial velocity, final velocity, and time interval between points A and B. If the athlete runs at a constant speed, their initial and final velocities will be the same, so the average acceleration will be zero.
Therefore, the component of the runner's average acceleration between points A and B is zero.
Note: These calculations assume that point A is at the top of the track and point B is at the bottom. If the positions of A and B are different, or if the dimensions or speed of the track are different, the results may vary.