A runner completes a 400 m race on a straight track. Her coach records split times at 100 m intervals. The results are shown in the table. The runner starts...
Question 1 Report
A runner completes a 400 m race on a straight track. Her coach records split times at 100 m intervals. The results are shown in the table. The runner starts from rest at the starting blocks. The track is level and the wind speed is zero on this day. The coach is studying how the runner's speed varies through the race to plan a better training programme for the next competition season.
| section | distance / m | time for section / s |
|---|---|---|
| 1st 100 m | 100 | 14.0 |
| 2nd 100 m | 100 | 12.0 |
| 3rd 100 m | 100 | 13.0 |
| 4th 100 m | 100 | 15.0 |
(a) Calculate the average speed during the 1st 100 m section. [2]
(b) Calculate the average speed during the 2nd 100 m section. [1]
(c) Calculate the average speed for the entire 400 m race. [2]
(d) State during which section the runner is fastest and suggest why the runner is slower in the final section. [2]
Answer Details
(a) Average speed during the 1st 100 m section
\(\text{average speed} = \frac{\text{distance}}{\text{time}} = \frac{100}{14.0}\) [1]
= 7.14 m/s (accept 7.1 m/s) [1]
(b) Average speed during the 2nd 100 m section
\(\text{average speed} = \frac{100}{12.0} =\) 8.33 m/s (accept 8.3 m/s) [1]
(c) Average speed for the entire 400 m race
Total time = 14.0 + 12.0 + 13.0 + 15.0 = 54.0 s
\(\text{average speed} = \frac{400}{54.0}\) [1]
= 7.41 m/s (accept 7.4 m/s) [1]
Note that the overall average speed is not the average of the four section speeds. Average speed is always total distance divided by total time.
(d) Fastest section and reason for slowing in the final section
The runner is fastest in the 2nd section, where her average speed is 8.33 m/s (the highest of the four). [1]
In the final section the runner is tiring: her muscles are fatiguing, meaning they can no longer maintain the same force output or power. This results in a reduced speed despite her effort. [1]
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