A car races at a constant speed of 25 m/s around a circular track with a radius of 150 meters. Consider 1/4 of a lap starting on the south side (heading east) and ending on the east side (heading north).
A. How much time does the car take to travel between the two points?
B. what is the displacement between starting and ending points?
C. What is the average velocity?
D. WHat is the change in velocity?
E. What is the average (vector) acceleration?
To answer these questions, we can use the formulas related to circular motion. Let's go step by step through each question:
A. To calculate the time it takes for the car to travel between the two points, we need to find the distance traveled first.
Since the car completes 1/4 of a lap, it covers an arc length of 1/4 of the circumference of the circular track.
The formula for the circumference of a circle is C = 2πr, where r is the radius.
Therefore, the distance traveled by the car is (1/4) * 2π * 150 meters.
Now, we can use the formula for time: time = distance / speed.
Substituting the values, we get: time = [(1/4) * 2π * 150] / 25 m/s.
B. The displacement between the starting and ending points can be found using the formula for arc length.
Since the car completes 1/4 of a lap, it travels 1/4 of the circumference of the circular track, which is 1/4 * 2π * 150 meters.
C. The average velocity can be calculated by dividing the displacement by the time taken to travel between the two points. So, average velocity = displacement / time.
D. The change in velocity can be found by subtracting the initial velocity from the final velocity. However, in this scenario, the car is moving at a constant speed, so the change in velocity is zero.
E. The average (vector) acceleration can be calculated by dividing the change in velocity by the time taken to travel between the two points. As mentioned earlier, the change in velocity is zero, so the average acceleration is also zero.
By following these explanations and using the appropriate formulas, you can calculate the answers to each of the questions.