A Porsche challenges a Honda to a 400-m race. Because the Porsche's acceleration of 3.5m/s2 is larger than the Honda's 3.0m/s2, 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?