Question

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?

Answer 1

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.