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 :)

## Best Answer

If the motorcycle starts at $x=0$ at $t=0s$, then the position of the motorcycle is given by

$x = 0.5·a·t^2$, dependent on time $t$.

The car starts at $x = -100m$ at $t=0s$ and is on time $t$ at

$x = -100m+vt$

for the velocity $v = 20m/s$. Now equate these equations to get

$-100m + vt = x = 0.5at^2$.

You can solve this quadratic equation, but maybe it can occur that you get negative numbers in square root, something which would be unphysical. The value of the discriminant (number under square root) must be positive; therefore you must search, when the discriminant is Zero (on this value of $v$ the Transition to unphysical solution, the negative discriminant, takes place).

That condition allows you to solve by $v$.