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## Homework Statement

A Porsche challenges a Honda to a 400-m race. Because the Porsche's acceleration of 3.5m/s

^{2}is larger than the Honda's 3.0m/s

^{2}, the Honda gets a 50-m head start. Both cars start accelerating at the same instant. Who wins?

## The Attempt at a Solution

The only thing I'm not sure about is how to get the velocity from a given acceleration. How do you figure it out mathematically?

Edit: So basically I set up both things as a function of time, and I integrated.

Porsche: a(t) = 3.5t

Porsche: v(t) = (3.5/2)t^2

Porsche: s(t) = (3.5/6)t^3

Honda: a(t) = 3t

Honda: v(t) = (3/2)t^2

Honda: s(t) = (1/2)t^3 + 50

Using these formulas, I calculated that the Porsche wins! Does it look correct?

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