Porsche challenges a Honda acceleration

[Zhalfirin88]

Homework Statement

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?

 

[rock.freak667]

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

your expressions for a(t) are wrong, they are constant and don't depend on time. So just redo the integration and find the time when the distance is 400m.

 

[Zhalfirin88]

Okay thanks, the Porsche still won ^_^. But anyways, is that how you'd normally solve it? I'm pretty sure there are other ways but that just seemed like the easiest and first thing that I thought of.

 

[rock.freak667]

Okay thanks, the Porsche still won ^_^. But anyways, is that how you'd normally solve it? I'm pretty sure there are other ways but that just seemed like the easiest and first thing that I thought of.

yes that is how you'd do it. Though instead of integrating you could have just used the direct result from the kinematic equation: s=1/2at²