If an 80kg sprinter can accelerate from a standing start to a speed of 10 m/s in 3s, what average power is generated
Final kinetic energy divided by time.
(1/2)MV^2/(3 s) = 1333 W
That is nearly two horsepower!
To calculate the average power generated by the sprinter, we can use the formula:
Power = Work / Time
First, let's calculate the work done by the sprinter. Since the sprinter starts from a standing start, we can assume that the work done is equal to the change in kinetic energy.
The formula for kinetic energy is:
Kinetic Energy = (1/2) * mass * velocity^2
The initial velocity is 0 since the sprinter starts from a standing start, and the final velocity is 10 m/s. The mass of the sprinter is 80 kg.
Kinetic Energy = (1/2) * 80 kg * (10 m/s)^2
Kinetic Energy = 0.5 * 80 kg * 100 m^2/s^2
Kinetic Energy = 4000 kg m^2/s^2
Since the work done is equal to the change in kinetic energy, the work done by the sprinter is 4000 kg m^2/s^2.
Now, let's calculate the average power. The time taken is 3 seconds.
Power = Work / Time
Power = 4000 kg m^2/s^2 / 3 s
Power ≈ 1333.33 W
Therefore, the average power generated by the sprinter is approximately 1333.33 watts.
To calculate the average power generated by the sprinter, we can use the formula:
Average Power = Work / Time
To calculate the work done by the sprinter, we need to find the change in kinetic energy. The formula for kinetic energy is given by:
Kinetic Energy = (1/2) * mass * velocity^2
Initially, the sprinter is at rest, so the initial kinetic energy is 0. The final kinetic energy can be calculated using the mass and final velocity given:
Final Kinetic Energy = (1/2) * mass * final velocity^2
The change in kinetic energy is then given by the difference between the final and initial kinetic energy:
Change in Kinetic Energy = Final Kinetic Energy - Initial Kinetic Energy
= (1/2) * mass * final velocity^2 - 0
= (1/2) * mass * final velocity^2
Now, we can calculate the work done using the formula:
Work = Change in Kinetic Energy
Finally, we can substitute the values given in the problem to find the average power:
Average Power = Work / Time
Substituting the values for mass (80 kg), final velocity (10 m/s), and time (3 s) into the equations, we can calculate the average power generated by the sprinter.