Answer:
There are a couple of ways to do this.
(i) Set up the two kinematics equations:
Honda: s = ½at² = ½ * 3m/s² * t² = 1.5m/s² * t²
Porsche: S = ½ * 3.5m/s² * (t - 1s)² = 1.75m/s² * (t - 1s)²
When does s = S ? Dropping units for ease,
1.5t² = 1.75(t-1)²
which is quadratic and has solutions at t = 0.5 s → which is no good, since it would leave the porsche with -0.5 s, which isn't possible, and
t = 13.5 s
When they've gone the same distance, they've gone
d = 1.5m/s² * (13.5s)² = 273 meters
The Porsche wins easily. ◄
Want to make it interesting? Give the Honda 1¼ seconds.
Then t = 16.85 s
and x = 1.5m/s² * (16.85s)² = 426 m
and the Honda squeaks out a victory.
You could also just find the time it takes each to go 400 m:
Honda: t = √(2s/a) = √(800m / 3.0m/s²) = 16.3 s
Porsche: T = √(800m / 3.5m/s²) = 15.1 s
Since the Porsche only gives up 1 s at the beginning, it wins by 0.2 s.
Explanation:
