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## Homework Statement

Our professor has tasked us to come up with a thought experiment to test the following scenario: "Two vehicles are going to race a fixed distance, both starting from rest. One vehicle has a greater maximum acceleration than the other, but a lower maximum speed. If both vehicles reach their top speed before completing the race, which vehicle will win?"

## Homework Equations

We are allowed to use any of the following four equations (plus the gravitational constant):

Δx = 1/2(v

_{0}+ v)t

Δx = v

_{0}t + 1/2at

^{2}

v = v

_{0}+ at

v

^{2}= v

_{0}

^{2}+ 2aΔx

g = 9.80 m/s

^{2}

Values for the first car:

Δx = fixed distance = 3300 m

v

_{0}= initial velocity = 0 m/s

v = final velocity = 240 km/h

a = acceleration = 3000 m/s

^{2}

Values for the second car:

Δx = fixed distance = 3300 m

v

_{0}= initial velocity = 0 m/s

v = final velocity = 280 km/h

a = acceleration = 2000 m/s

^{2}

## The Attempt at a Solution

To be honest, these values were chosen by me. I have no idea how to determine which car would win in a 3.3 km race (3300 m) given the above values. What stumps me is which equation to use to determine the result of the experiment.