High School

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A 114 kg fullback runs at the line of scrimmage.

(a) Find the constant force that must be exerted on him to bring him to rest in a distance of 1.1 m in a time interval of 0.29 s. The force should be opposite the fullback's direction of motion.

Answer :

Final answer:

To determine the acceleration and force exerted by a soccer player to reach top speed, we apply kinematics to calculate the average acceleration, which is 3.20 m/s², and dynamics with Newton's second law to calculate the average force, which is 224 Newtons.

Explanation:

The question involves a soccer player who starts from rest and accelerates to a certain velocity. To solve this problem, we need to apply the principles of kinematics and dynamics.

  • Part (a) - Average Acceleration

We can calculate the average acceleration (a) using the formula:

a = ∆v / ∆t

Where ∆v is the change in velocity and ∆t is the change in time. Given the final velocity (v) is 8.00 m/s and the time (t) is 2.50 s, we find the acceleration to be:

a = 8.00 m/s / 2.50 s = 3.20 m/s²

  • Part (b) - Average Force

To find the average force (F) exerted by the soccer player, we use Newton's second law:

F = m * a

Here, m is the mass of the player, which is 70.0 kg, and a is the acceleration we just calculated.

F = 70.0 kg * 3.20 m/s²

= 224 N

Therefore, the average force the player must exert backward on the ground is 224 Newtons.

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