A football punter accelerates a football from rest to a speed of 7 m/s during the time in which his toe is in contact with the ball (about 0.26 s). If the football has a mass of 0.50 kg, what average force does the punter exert on the ball?

I will be happy to critique your thinking.

To find the average force exerted by the punter on the ball, we can use Newton's second law of motion, which states that force is equal to mass times acceleration:

Force = Mass × Acceleration

In this case, the mass of the football is given as 0.50 kg, and we need to find the acceleration.

To find the acceleration, we can use the equation for average acceleration:

Acceleration = Change in velocity / Time

Given that the ball starts from rest (initial velocity = 0 m/s) and reaches a final speed of 7 m/s, the change in velocity is:

Change in velocity = Final velocity - Initial velocity
Change in velocity = 7 m/s - 0 m/s
Change in velocity = 7 m/s

The time taken for this change in velocity is given as 0.26 seconds.

Now we can calculate the average acceleration:

Acceleration = Change in velocity / Time
Acceleration = 7 m/s / 0.26 s
Acceleration ≈ 26.9 m/s²

Now that we have the acceleration, we can substitute it back into Newton's second law to find the force:

Force = Mass × Acceleration
Force = 0.5 kg × 26.9 m/s²
Force ≈ 13.44 N

Therefore, the average force exerted by the punter on the ball is approximately 13.44 N.