What average power is required for a runner with a mass of 80 kg to reach a speed of 8.2 m/s during a time of 1.8 s?
To calculate the average power required for the runner to reach a speed of 8.2 m/s, we can use the equation:
Power = Work / Time
The work done on the runner can be calculated using the equation:
Work = Change in kinetic energy
The change in kinetic energy can be calculated using the equation:
Change in kinetic energy = (1/2) * mass * (final velocity^2 - initial velocity^2)
In this case, the initial velocity is assumed to be 0 since the runner starts from rest.
Let's break down the calculation step by step:
1. Calculate the change in kinetic energy:
Change in kinetic energy = (1/2) * 80 kg * (8.2 m/s)^2 - (0 m/s)^2
= (1/2) * 80 kg * (8.2^2) J
2. Calculate the average power:
Power = Work / Time
= (1/2) * 80 kg * (8.2^2) J / 1.8 s
Now, you can plug in the values and calculate the average power required for the runner to reach a speed of 8.2 m/s during a time of 1.8 s.