Question

In Michael Johnson's world-record 400 m sprint, he ran the first 100 m in 11.20 s; then he reached the 200 m mark after a total time of 21.32 s had elapsed, reached the 300 m mark after 31.76 s,and finished in 43.18 s.

During what 100 m segment was his speed the highest?

a) Between the start and the 100 m mark.

b) Between the 100 m mark and the 200 m mark.

c) Between the 200 m mark and the 300 m mark.

d)Between the 300 m mark and the finish.

Answer 1

The highest speed in Michael Johnson's world-record 400 m sprint was achieved during the segment between the 100 m mark and the 200 m mark with a speed of 9.88 m/s.

Step-by-step explanation:

To determine which 100 m segment Michael Johnson had the highest speed, we should calculate his speed for each segment separately. Speed is calculated by dividing the distance by the time taken to cover that distance. We are given the total time at each 100 m interval, so we need to calculate the time for each interval separately and then calculate the speed.

• For the first 100 m: Speed = 100 m / 11.20 s = 8.93 m/s
• For the second 100 m (100 m to 200 m): Time taken = 21.32 s - 11.20 s = 10.12 s, so Speed = 100 m / 10.12 s = 9.88 m/s
• For the third 100 m (200 m to 300 m): Time taken = 31.76 s - 21.32 s = 10.44 s, so Speed = 100 m / 10.44 s = 9.58 m/s
• For the fourth 100 m (300 m to 400 m): Time taken = 43.18 s - 31.76 s = 11.42 s, so Speed = 100 m / 11.42 s= 8.76 m/s

Comparing these speeds, we can see that the highest speed was achieved during the segment between the 100 m mark and the 200 m mark.

Answer 2

b)

Step-by-step explanation:

Assuming that we are talking about average speed during any segment, we can apply the definition of average speed, as follows:

v(avg) = Δx / Δt = (xf-x₀) / (tfi-t₀)

Using this definition for the 4 segments, we have:

1) v(0-100m) = 100 m / 11.20 sec = 8.93 m/s

2) v(100m-200m) = 100 m / (21.32 s - 11.2 s) = 100 m / 10.12 s = 9.88 m/s

3) v(200m -300m) = 100 m / (31.76 s- 21.32s) = 100 m / 10.44 s = 9.58 m/s

4) v(300m-400m) = 100 m / (43.18 s - 31.76 s) = 100 m / 11.42 s = 8.76 m/s

As we can see, the highest speed was reached between the 100m mark and the 200m mark, so the statement b) is the one that results to be true.