Aworld-class sprinter running a 100 m dash was clocked at 5.4 m/s 1.0 s after starting running and at 9.8 m/s 1.5 s later. in which of these time intervals, 0 to 1.0 s or 1.0 s to 2.5 s, was his output power greater?

The output power is greater in the interval from 1.0 s to 2.5 s

Explanation:

Physical Power

It measures the amount of work W an object does in certain time t. The formula needed to compute power is

Work can be computed in several ways since we are given the motion conditions, we'll use this formula, for F= applied force, x=distance parallel to F

The second Newton's law gives us the net force as

being m the mass of the object and a the acceleration it has for a given period of time. In our problem, we have two different behaviors for each interval and we must calculate this force since the acceleration is changing. Let's calculate the acceleration in the first interval. We can use the formula for the final speed vf knowing the initial speed vo (which is 0 because the sprinter starts from rest), the acceleration a, and the time t:

Solving for a

The distance traveled in the interval is given by

Since vo=0

The force is given by

We don't know the value of m, so the force is

Computing the work done by the sprinter

The power is finally computed

During the second interval, from t=1 sec to 1.5 sec, the speed changes from 5.4 m/s to 9.8 m/s. This allows us to compute the second acceleration

The distance is

The net force is

The work done by the sprinter is now computed as

At last, the output power is

By comparing both results, and being m the same for both parts, we conclude the output power is greater in the interval from 1.0 s to 2.5 s

v=ir = 3x15 =45 v

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