who will win a race between man, horse and car of same power Other day I got into a chat with my friend on work power and energy where he asked an intelligence related question the question was like this 

if a race was conducted between a man a horse and a car of SAME POWER then who will most probably win the race

and to his question i answered that obviously man could win it because the definition of power states that

power is the fraction of work done in a given time 

and as per the definition of work it is described as the dot product of force and displacement 
and from newton's second law we get F=ma 
the displacement of all the three is same as their end point. so the product of mass and acceleration must be same for all and in this situation a normal man will have less weight than horse and car so it clearly states that acceleration must be of more magnitude for man.
but to my surprise he said my answer is wrong and he did'nt explained how it was wrong 
am i really wrong? please guide me if i am wrong in which aspect.
 A: Let's work through this problem... 
$$\text{Power} = \frac{\text{Work}}{\text{Time}} \; \text{and} \; \text{Work} = \text{Force}\cdot \text{Displacement} $$
therefore
$$\text{Power} = \frac{\text{Force}\cdot\text{Displacement}}{\text{Time}} $$
From Newton's Second law we know 
$$\text{Force} = \text{Mass}\cdot\text{Acceleration}$$
Substituting again: 
$$\text{Power} = \frac{\text{Mass}\cdot\text{Acceleration}\cdot\text{Displacement}}{\text{Time}}$$
Now the only things that will differ in your set up is the mass (since you want to know the greatest acceleration) 
$$ \text{Mass} = \frac{\text{Power}\cdot\text{Time}}{\text{Acceleration}\cdot\text{Displacement}}$$
This relationship implies that, all others held constant, to get a greater acceleration you have a smaller mass. So the Man would win because in the same amount of time he can accelerate to a greater velocity. 
You were right and your friend was probably just mad he was wrong :) 
A: 
in this situation a normal man will have less weight than horse and car so it clearly states that acceleration must be same.

No. If the force is the same for all 3, then if the mass is different, the acceleration must be different. Since the man has the least mass, then he will accelerate the fastest. So the man would win the race.
But in the real world, a man cannot develop 1 hp using his legs (I think it is about 0.6 hp). A house would develop 1 hp and a car is usually rated over 80 hp. It would certainly be difficult to say whether a horse or a car would win a short race (a car has a faster top speed so it will win a long race).
A race between horses and men. Another race.
