Question

A race car completes the final lap of a race on a 2-kilometer circular track. At the start of the lap, it crosses the line at 60 meters/second. It completes the lap 28.57 seconds later, crossing the line at 85 meters/second. Calculate the displacement and average acceleration of the car along the track over the course of the final lap.

Answer 1

The displacement of the race car after completing the lap is 0 meters since it returns to the starting point. The average acceleration is calculated to be approximately 0.875 m/s² using the change in velocity (25 m/s) over the time taken (28.57 seconds).

Step-by-step explanation:

The student is asking about the displacement and average acceleration of a race car over the final lap of a race. To find the displacement, we note that since the track is circular and the car completes a lap, the displacement is 0 meters because the car returns to its starting point. The average acceleration can be calculated using the formula a = (vf - vi) / t, where vi is the initial velocity (60 m/s), vf is the final velocity (85 m/s), and t is the time taken (28.57 seconds).

To calculate the average acceleration:

1. Subtract the initial velocity from the final velocity: 85 m/s - 60 m/s = 25 m/s.
2. Divide the change in velocity by the time taken: 25 m/s / 28.57 s = approximately 0.875 m/s².

The average acceleration of the car is approximately 0.875 m/s².

Answer 2

The displacement of the race car is 2 km and the average acceleration is 0.87 m/s².

Step-by-step explanation:

To calculate the displacement of the race car, we need to find the difference between the position vectors of the starting and ending points.

The starting position vector is 0 km since the car starts at the line, and the ending position vector is the circumference of the track, which is 2 km.

Therefore, the displacement is 2 km - 0 km = 2 km.

To calculate the average acceleration of the race car, we can use the formula:

Average acceleration = (final velocity - initial velocity) / time

Here, the final velocity is 85 m/s, the initial velocity is 60 m/s, and the time is 28.57 seconds. Plugging these values into the formula, we can calculate the average acceleration to be:

Average acceleration = (85 m/s - 60 m/s) / 28.57 s = 0.87 m/s².