Final answer:
The average force exerted by the sprinter is 240 N, calculated using Newton's second law of motion, with an average acceleration of 3.0 m/s² and the sprinter's mass of 80.0 kg.
Step-by-step explanation:
The question is regarding the average force a sprinter must exert to achieve a certain acceleration. To calculate the average force exerted by the sprinter, we can use Newton's second law of motion, which states that force equals mass times acceleration (F = ma).
From the information given, the sprinter accelerates from rest to 9.0 m/s in 3 seconds. Thus, the average acceleration (a) can be calculated using the formula a = Δv / Δt, where Δv is the change in velocity and Δt is the time interval. Here, the change in velocity (Δv) is 9.0 m/s (since the initial velocity was 0 m/s) and the time interval (Δt) is 3 seconds. Therefore, the average acceleration is 9.0 m/s ÷ 3 s = 3.0 m/s².
The mass (m) of the sprinter is 80.0 kg. Plugging the values into Newton's second law gives us the average force exerted by the sprinter: F = 80.0 kg × 3.0 m/s² = 240 N. The sprinter exerts an average force of 240 N backward on the track.