Calculate the average force a 60.0-kg sprinter exerts backward on the track to accelerate from 2.00 to 8.00 m/s in a distance of 2.50m

Hi there!

Because of Newton's Third Law, the force exerted by the sprinter on the track is equal and opposite to the force exerted by the track on the sprinter.

We can begin by calculating the sprinter's acceleration. Use the equation:

vf² = vi² + 2ad

Rearrange for acceleration:

(vf² - vi²)/2d = a

Plug in values:

(8² - 2²)/2(2.5) = 60/5 = 12 m/s²

Calculate the force:

∑F = ma

∑F = 60 × 12 = 720 N. This is the amount of force exerted by the track on the sprinter in causing him to accelerate forward.

Thus, the backward force exerted by the sprinter on the track is the opposite, or -720 N.

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