Final answer:
The average speed for the lap is (40π m) / (64.0 s). The average velocity for the lap is zero. The average speed for the first half-lap is (20π m) / (28.9 s). The average velocity for the first half-lap is zero.
Step-by-step explanation:
a. To calculate the average speed, we can use the formula:
Average Speed = Total Distance / Total Time
In this case, the total distance covered in one lap is the circumference of the circular track, which can be calculated using the formula:
Circumference = π x diameter
Substituting the given diameter of 40.0 m, we get a circumference of 40π m. The total time taken to cover one lap is given as 64.0 s.
Therefore, the average speed is: Average Speed = (40π m) / (64.0 s)
b. Average velocity is calculated as the displacement divided by the total time. In this case, the average velocity for one lap is zero since the runner returns to the starting point and has no net displacement.
c. To calculate the average speed for the first half-lap, we can use the formula:
Average Speed = Total Distance / Total Time
The total distance covered for the first half-lap is half the circumference of the circular track, which can be calculated using the formula:
Circumference = π x diameter
Substituting the given diameter of 40.0 m, we get a circumference of 20π m. The total time taken to cover the first half-lap is given as 28.9 s.
Therefore, the average speed for the first half-lap is: Average Speed = (20π m) / (28.9 s)
d. Since the runner covers the first half-lap, there is no net displacement and the average velocity for the first half-lap is zero.