Concept explainers
A runner completes 6½ laps around a 400 m track during a 12 min (720 s) run test. Calculate the following quantities:
a. The distance the runner covered
b. The runner’s displacement at the end of 12 min
c. The runner’s average speed
d. The runner’s average velocity
e. The runner’s average pace (Answers: a. 2.6 km; b. 160 m; c. 3.6 m/s; d. 0.22 m/s; e. 4.6 min/km)
a)
To determine: The distance runner covered.
Answer to Problem 1IP
The distance covered by the runner is
Explanation of Solution
Calculation:
Express the distance covered by the runner.
Substitute
Therefore, distance covered by the runner is
Therefore, distance covered by the runner is
b)
To determine: The runner’s displacement at the end of 12 min.
Answer to Problem 1IP
Displacement by the runner at the end of 12 min is
Explanation of Solution
Calculation:
At 12 min runner completes 6.5 laps and the runner will be at the position of 0.5 lap.
Consider each side of the track is 100 m.
Use Pythagoras theorem to express the runner’s displacement at the end of 12 min.
Substitute
Therefore, displacement by the runner at the end of 12 min is
Therefore, displacement by the runner at the end of 12 min is
c)
To determine: The runner’s average speed.
Answer to Problem 1IP
The average speed of the runner is
Explanation of Solution
Calculation:
Express the average speed of the runner.
Substitute 2600 m for total distance and 12 min to find the average speed.
Therefore, average speed of the runner is
Therefore, average speed of the runner is
d)
To determine: The runner’s average velocity.
Answer to Problem 1IP
The average velocity of the runner is
Explanation of Solution
Calculation:
Express the average velocity of the runner.
Substitute 141.4 m for total displacement and 12 min to find the average velocity.
Therefore, average velocity of the runner is
Therefore, average velocity of the runner is
e)
To determine: The runner’s average pace.
Answer to Problem 1IP
The average pace of the runner is
Explanation of Solution
Calculation:
Express the average pace of the runner.
Substitute
Therefore, average pace of the runner is
Therefore, average pace of the runner is
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