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.