Sprinting near the end of a race, a runner with a mass of 70 kg accelerates from a speed of 6 m/s to a speed of 9 m/s in 2 s.
(a) What is the runner's average acceleration during this time?
(b) To gain speed the runner produces a backward force on the ground, so that the ground pushes the runner forward providing the force necessary for acceleration. Calculate this average force.
To find the average acceleration of the runner, we can use the formula:
Average acceleration = (Change in velocity) / (Time taken)
Given:
Initial velocity (u) = 6 m/s
Final velocity (v) = 9 m/s
Time (t) = 2 s
(a) Average acceleration = (9 m/s - 6 m/s) / 2 s
Step 1: Calculate the change in velocity
Change in velocity = 9 m/s - 6 m/s = 3 m/s
Step 2: Calculate the average acceleration
Average acceleration = 3 m/s / 2 s
Average acceleration = 1.5 m/s²
Therefore, the runner's average acceleration during this time is 1.5 m/s².
To find the average force exerted by the ground on the runner, we can use Newton's second law of motion:
Force (F) = Mass (m) × Acceleration (a)
Given:
Mass (m) = 70 kg (as mentioned in the problem)
Acceleration (a) = 1.5 m/s² (calculated in part a)
(b) Average force = Mass × Acceleration
Average force = 70 kg × 1.5 m/s²
Step 1: Calculate the average force
Average force = 105 N
Therefore, the average force exerted by the ground on the runner is 105 Newtons.
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