Final answer:
By applying Newton's second law of motion, the sprinter's acceleration is calculated to be approximately 7.07 m/s². The closest answer choice provided is (a) 6.92 m/s².
Step-by-step explanation:
When the 82.6 kg sprinter exerts an average force of 584 N backward on the ground for 0.843 s, we can determine the sprinter's acceleration by using Newton's second law of motion, which states that force equals mass times acceleration (F = ma). To find the acceleration, we rearrange the formula to a = F / m.
The sprinter's mass (m) is 82.6 kg, and the force exerted (F) is 584 N. Placing these values into the equation gives us a = 584 N / 82.6 kg, which equals approximately 7.07 m/s². However, as the options provided do not include 7.07 m/s², we can evaluate the closest value which would be option (a) 6.92 m/s².