# Porsche challenges a Honda acceleration

## 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?

Last edited:

rock.freak667
Homework Helper

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.

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
Homework Helper

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