physics題超難!!!

I think this is a cert. level question. In cert. level, sometimes, a question is asked to test how you can relate the theory to a real situation. The question talks about the world record of 100m running. And it does not say air resistance or friction is negligible. So, you should consider this question a real situation that the runner attains his maximum speed in first few seconds. Then he keeps more or less the same speed until he finishes. Also, air restistance and friction are not negligible.

If so, obviously, the acceleration is not constant. So, you cannot use the formula v²-u²=2as, which applies to constant acceleration (or constant external force) situation only. So, Method 1, which assumes a constant acceleration without air resistance or friction, is wrong.

Actually, the question gives you a clue through the key word average in the sentence the force he applied is 170N on average. The word average implies that the force he applied may not be constant, hence acceleration may not be constant too. In cert. level, non-constant acceleration is not yet taught. But the question only asks the average power and the formula P = Fv is still valid if you consider the average of P, F and v. So, Method 2 is the only valid way to find out the average power.

This is a good typical question and it tests you when to use the right formula. I believe you know the formulas well. So, make sure that you know the exact meaning of the variables and the conditions of the formulas before you apply them.

Hope that this can help you. As you ask in English, I reply in English. You are welcome to comment and I'll try my best to answer.

2007-06-29 11:27:11 補充：
Sorry, the question may neglect friction or air resistance. Then P = Fv will be the average useful power. But still you cannot use Method 1 because the question does not say that the force the runner applied is a constant.

2007-06-29 11:27:22 補充：
But the question is then strange and not realistic. Maybe, it just uses the wrong word. Maybe, it is asking either the average delivered power or he horizontal component of the force the runner exerted is 170N on average.

In method 1, you assume the runner to accelerate from t = 0 to t = 9.79 s, and you calculate the final velocity of the runner to be 20.4289 m/s. If you use the final velocity to calculate the K.E. of the runner and then calculate the power by dividing K.E. by 9.79, you will assume the runner to run at the final velocity in the whole journey !

In the formulae of the power of the runner, P = F x V, V is the instantaneous velocity of the runner. If the runner apply F = 170 N and run at V, he has power P = F x V at the time of running at V. In method 2, you neglect the acceleration of the runner and assume he running at uniform velocity of 10.21 m/s, the power you calculated is the average power of the runner.

Therefore, you should use method 2 to calculate the power.

If you do not want to use 170 N to get the answer, you must firstly calculate the K.E. But, you must know the velocity change of the runner and determine when he will stop to accelerate and run at uniform speed.