While running, a person dissipates about 0.60 J of mechanical energy per step per kilogram of body mass. If a 61 kg person develops a power of 65 W during a race, how fast is the person running? Assume that a running step is 1.5 m long.

2.66m/s

Explanation:

information we have

power: 65W

work per step per kilogram: 0.60J

mass: 61kg

length of a running step: 1.5m

---------------

the formula for power is:

where W is the work and t is time.

time is also defined as:

so substituting this into the formula for power we get:

where v is the velocity we are looking for, d is the distance per step: , W is the work per step and P is power .

we know that the work per step per kilogram is:

0.60J

so to find the work per step of his whole body we need to multiply the 0.60J by the 61 kilograms of his mas:

this is the work per step of the person.

So now we can calculate the velocity using the formula for power

clearing for v:

and substituting known values: