compare your average speed in the following cases.

a. you walk 73.2 m at a speed of 1.2 m/s and then run 73.2 m at a speed of 3.1 m/s along a straight track.

b. you walk 1 min. at a speed of 1.2 m/s and then run for 1 min. at 3.1 m/s along a straight track.

To compare the average speeds in each case, we need to calculate the average speed for each portion of the journey and then calculate the overall average speed.

Case a:
1. Walking distance: 73.2 m
Speed of walking: 1.2 m/s
Time taken for walking = Distance/Speed = 73.2 m / 1.2 m/s = 61 seconds

2. Running distance: 73.2 m
Speed of running: 3.1 m/s
Time taken for running = Distance/Speed = 73.2 m / 3.1 m/s = 23.61 seconds

Overall time taken = Time taken for walking + Time taken for running = 61 seconds + 23.61 seconds = 84.61 seconds

Overall distance covered = Walking distance + Running distance = 73.2 m + 73.2 m = 146.4 m

Overall average speed = Overall distance / Overall time = 146.4 m / 84.61 s ≈ 1.73 m/s

Case b:
1. Walking time: 1 min = 60 seconds
Speed of walking: 1.2 m/s
Distance covered while walking = Speed x Time = 1.2 m/s x 60 s = 72 m

2. Running time: 1 min = 60 seconds
Speed of running: 3.1 m/s
Distance covered while running = Speed x Time = 3.1 m/s x 60 s = 186 m

Overall distance covered = Distance covered while walking + Distance covered while running = 72 m + 186 m = 258 m

Overall time taken = Walking time + Running time = 60 seconds + 60 seconds = 120 seconds

Overall average speed = Overall distance / Overall time = 258 m / 120 s ≈ 2.15 m/s

Comparing the two cases:
Case a: Average speed = 1.73 m/s
Case b: Average speed = 2.15 m/s

Therefore, the average speed in case b (walking for 1 minute then running for 1 minute) is higher than the average speed in case a (walking 73.2 m and then running 73.2 m).

To compare the average speeds in the given cases, we need to calculate the total distance traveled and the total time taken.

a. In the first case, you walk 73.2 m at a speed of 1.2 m/s, which takes `(73.2 m) / (1.2 m/s) = 61 seconds`. Then, you run another 73.2 m at a speed of 3.1 m/s, which takes `(73.2 m) / (3.1 m/s) = 23.61 seconds`. Therefore, the total time taken is `61 seconds + 23.61 seconds = 84.61 seconds`.

To calculate the total distance traveled, we add the distances covered during walking and running: `73.2 m + 73.2 m = 146.4 m`.

The average speed is calculated by dividing the total distance by the total time: `(146.4 m) / (84.61 seconds) ≈ 1.73 m/s`.

b. In the second case, you walk for 1 minute at a speed of 1.2 m/s, which covers `(1.2 m/s) * (60 seconds) = 72 m`. Then, you run for 1 minute at a speed of 3.1 m/s, which covers `(3.1 m/s) * (60 seconds) = 186 m`.

The total distance traveled is `72 m + 186 m = 258 m`.

Since the total time taken is 2 minutes, the average speed is `(258 m) / (2 minutes) = 129 m/minute`.

To compare the average speeds in both cases:

Case a: Average Speed ≈ 1.73 m/s
Case b: Average Speed ≈ 129 m/minute

We can see that the average speed in case b is higher than the average speed in case a.

(a)since time=distance/speed, you have

total distance: 73.2+73.2=146.4m
total time: 73.2/1.2 + 73.2/3.1 = 84.6s
avg speed: 146.4m/84.6s = 1.73 m/s

do (b) the same way