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## A Porsche challenges a Honda to a 400 m race. Because the Porsche’s acceleration is 3.50 m/s2 is larger than the Honda’s 3.00 m/s2 , the Hon

Question

A Porsche challenges a Honda to a 400 m race. Because the Porsche’s acceleration is 3.50 m/s2 is larger than the Honda’s 3.00 m/s2 , the Honda gets a 1.00 s head start. Who wins? By how many seconds?

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Physics
3 years
2021-07-14T03:27:18+00:00
2021-07-14T03:27:18+00:00 1 Answers
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## Answers ( )

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: