A 70 kg human sprinter can accelerate from rest to 10 m/s in 3.0 s . During the same time interval, a 30 kg greyhound can go from rest to 20 m/s . What is the average power output of each? Average power over a time interval ∆t is ∆E/∆t .

Video transcript

Hey, everyone. So this problem is dealing with power. Let's see what they're asking us. We have an 85 kg sprinter that accelerates from rest to a peak speed of 9.2 m per second in four seconds. A 65 kg Cheetah accelerates from rest to 27 m/s in just three seconds. We're asked to determine the mean power output of the sprinter and the Cheetah. And they give us this freight hint where the expression for average power is delta E over delta T where delta T is the time interval. So if you didn't recall that power is given by delta T over delta E, they give it to us in this problem and then from there because we have no external influences on the system, we can recall that delta E or change in energy is going to equal delta K, which is our kinetic energy from there. We can recall that delta K is given as one half M V F squared minus one half M V I squared. Both of the, both the sprinter and the Cheetah start from rest. So our V I is zero in both cases. And so from here, all we have to do is solve for our power plugging in this equation. And we're gonna do it twice, once for the sprinter and once for the cheating. So the power of the sprinter is going to equal the mass of the sprinter times the file velocity of the sprinter squared over two times that change in time of the sprinter. So in the problem, the mass of the sprinter is given as 85 kg. Our final speed is given as 9.2 m/s. And that quantity is squared Over two multiplied by our change in time, which was given as four seconds. We plug that in and we get and 99 watts. And so that is the answer for part one from our multiple choice options. We can see that a sprinter equals 899 watts is the only one that has the correct answer for the sprinter. But let's finish out the problem to make sure that we are on the right track power for the Cheetah. It's going to be given as of the Cheetah times the bio velocity of the Cheetah squared over two multiplied by delta T G M mass, the Cheetah. And the problem was given As 65 kg. Our final speed of the Cheetah was given us 27 m/s. That quantity is squared all over two multiplied by our delta T of the Cheetah which was given as three seconds, we plug that in to me or left With 7.9 kW. And that does align with part B of answer A and so answer A is the correct answer for this problem. So that's all we have for this one. We'll see you in the next video.