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.
