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Novosadov [1.4K]
4 years ago
8

A Porsche challenges a Honda to a 400 m race. Because the Porsche’s acceleration of 3.5 m/s 2 is larger than the Honda’s 3.0 m/s

2, the Honda gets a 100-m head start—it is only 300 m from the finish line. Assume, somewhat unrealistically, that both cars can maintain these accelerations the entire distance. Who wins, and by how much time?
Physics
1 answer:
Karo-lina-s [1.5K]4 years ago
4 0

Explanation:

It is given that,

For Honda:

Initial velocity, u = 0

Initial position, x_i=0

Final position, x_f=300\ m

Acceleration, a=3\ m/s^2

Let t is the time taken by Honda. Using second equation of motion as :

x_f=x_i+ut+\dfrac{1}{2}at^2

300=0+0+\dfrac{1}{2}\times 3t^2

t = 14.14 seconds

For Porsche’s :

Initial velocity, u = 0

Initial position, x_i=0

Final position, x_f=400\ m

Acceleration, a=3.5\ m/s^2

Let t' is the time taken by Honda. Using second equation of motion as :

x_f=x_i+ut+\dfrac{1}{2}at'^2

400=0+0+\dfrac{1}{2}\times 3.5t^2

t' = 15.11 seconds

Since, the time taken by Honda is less while the time taken by Porsche's is more. So, Honda wins the race by (15.11 - 14.14 = 0.97) seconds. Hence, this is the required solution.

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