How much power is generated by a 90 kg sprinter that accelerates up to 9.0 m/s in 2.8 seconds?
To calculate the power generated by a sprinter, we need to use the formula:
Power (P) = Force (F) × Velocity (V)
First, we need to calculate the force exerted by the sprinter. We can use Newton's second law of motion, which states:
Force (F) = Mass (m) × Acceleration (a)
Given:
Mass (m) = 90 kg
Acceleration (a) = change in velocity / time
To find the change in velocity, we can subtract the initial velocity (0 m/s) from the final velocity (9.0 m/s):
Change in velocity = 9.0 m/s - 0 m/s = 9.0 m/s
From there, we can calculate the acceleration:
Acceleration (a) = change in velocity / time = 9.0 m/s / 2.8 s
Now, plug in the values to calculate the acceleration:
Acceleration (a) = 9.0 m/s / 2.8 s ≈ 3.21 m/s²
Next, we can calculate the force:
Force (F) = Mass (m) × Acceleration (a) = 90 kg × 3.21 m/s²
Now that we have the force, we can calculate the power by multiplying it with the velocity:
Power (P) = Force (F) × Velocity (V) = (90 kg × 3.21 m/s²) × 9.0 m/s
Calculate the power:
Power (P) = (90 kg × 3.21 m/s²) × 9.0 m/s ≈ 2591.1 Watts
Therefore, the power generated by the sprinter is approximately 2591.1 Watts.