Question

A sprinter of mass 80.0 k g accelerates from rest to 9.0 m / s on a flat track in 3 s . in the following treat the effect of air resistance to be negligible. include units as is his power output (also called useful power out) during this time?

Answer 1

The power output of an 80.0 kg sprinter accelerating from rest to 9.0 m/s in 3 seconds is 1080 Watts or approximately 1.45 horsepower.

Step-by-step explanation:

The problem is about calculating the power output of a sprinter with a mass of 80.0 kg who accelerates from 0 to 9.0 m/s over a period of 3 seconds.

First, we need to calculate the work done by the sprinter, which is equal to the change in kinetic energy. The kinetic energy (KE) can be calculated using the formula KE = 0.5 * m * v^2, where m is the mass and v is the velocity of the sprinter.

Initial KE = 0.5 * 80.0 kg * (0 m/s)^2 = 0 J
Final KE = 0.5 * 80.0 kg * (9.0 m/s)^2 = 0.5 * 80.0 kg * 81 m^2/s^2 = 3240 J

The work done, which is the change in kinetic energy, is therefore: Work = Final KE - Initial KE = 3240 J - 0 J = 3240 J.

Now, power is defined as work done over time. To find the power output, we divide the work done by the time it takes to do the work.
Power = Work / Time = 3240 J / 3 s = 1080 Watts.

To convert this to horsepower, we use the conversion factor 1 horsepower = 746 watts. So, the power output in horsepower is:
Power = 1080 Watts / 746 Watts/horsepower = ~1.45 horsepower.