A man is running around a circular track that is 200m in circumference. An observer

uses a stopwatch to record the runner’s time at the end of each lap, obtaining the
data in the tale below.
a. What was the man’s average speed (rate) between 68 s and 152 s?
b. What was the man average speed between 263 s and 412 s?
c. Calculate the man’s speed for each lap. Is he slowing down, speeding up or
neither?

I want an answer pls.

To calculate the man's average speed between two time intervals, we need to divide the total distance covered in that time by the duration.

a. To find the man's average speed between 68 s and 152 s, we need to first find out how many laps he completed in that time. Since the track is 200m in circumference, we can calculate:

Number of laps = Distance / Circumference
= 200m / 200m
= 1 lap

The man completed one lap between 68 s and 152 s. Therefore, the distance covered in this time period is equal to the circumference of the track, which is 200m.

Average speed = Distance / Time
= 200m / (152s - 68s)
= 200m / 84s
= 2.38 m/s

So, the man's average speed between 68 s and 152 s is 2.38 m/s.

b. Similarly, to find the man's average speed between 263 s and 412 s, we need to find the number of laps completed in this duration.

Number of laps = Distance / Circumference
= 200m / 200m
= 1 lap

Again, the man completed one lap between 263 s and 412 s. Therefore, the distance covered in this time period is 200m.

Average speed = Distance / Time
= 200m / (412s - 263s)
= 200m / 149s
= 1.34 m/s

So, the man's average speed between 263 s and 412 s is 1.34 m/s.

c. To calculate the man's speed for each lap, we need the times recorded for each lap. However, the data table for the lap times is not provided in the question. Without the lap times, we cannot calculate the speed for individual laps or determine if he is slowing down, speeding up, or neither.

To calculate average speed, we need to use the formula:

Average Speed = Total Distance / Total Time

a. To find the man's average speed between 68 s and 152 s:
1. Calculate the total distance covered during this time.
Since the track's circumference is 200m, the man will cover the same distance in each lap.
Number of laps covered = (152 s - 68 s) / (time taken for one lap)
First, we need to calculate the time taken for one lap.
The time taken for one lap = Time of first lap - Time of previous lap
= 68 s - 0 s
= 68 s
Number of laps covered = (152 s - 68 s) / (68 s)
= 84 s / 68 s
= 1.235 laps
Total distance covered = Number of laps * Circumference of the track
= 1.235 * 200 m
= 247 m

2. Calculate the total time taken during this period.
Total time = 152 s - 68 s
= 84 s

3. Calculate the average speed.
Average Speed = Total Distance / Total Time
= 247 m / 84 s
= 2.94 m/s (rounded to two decimal places)

b. To find the man's average speed between 263 s and 412 s:
Follow the same steps as in part (a) to calculate the average speed.

c. To calculate the man's speed for each lap:
1. Subtract the time taken for each lap from the time of the previous lap to find the lap time.
2. Divide the circumference of the track by the lap time to calculate the speed for each lap.

To determine if the man is slowing down, speeding up, or neither, compare the speeds of consecutive laps. If the speed increases, he is speeding up. If it decreases, he is slowing down. If the speeds remain relatively constant, he is maintaining a steady speed.