6. You have kinetic energy when you run. If you run three times as fast, you'll have a kinetic energy ____________________.

A) 3 times as much.
B) 6 times as much.
C) 9 times as much.
D) that is the same.
E) None of these.

replace v with 3v

KE = 1/2*m(3v)^2 = 1/2 * m * 9v^2

KE is multiplied by 9.

B) 6 times as much.

To determine the relation between the kinetic energy and running speed, we need to recall the formula for kinetic energy. The formula for kinetic energy is given by:

KE = (1/2) * m * v^2

Where KE represents the kinetic energy, m represents the mass of the object, and v represents the velocity or speed of the object.

In this case, we are assuming that the mass of the runner is constant. Therefore, the only variable that changes is the running speed (v).

If you run three times as fast, the new velocity will be three times the initial velocity. To find out how kinetic energy changes, we can substitute the new velocity into the formula and compare it to the initial kinetic energy.

Initial Kinetic Energy = (1/2) * m * v^2
New Kinetic Energy = (1/2) * m * (3v)^2 = (1/2) * m * 9v^2

Comparing the new kinetic energy to the initial kinetic energy:

New Kinetic Energy / Initial Kinetic Energy = [(1/2) * m * 9v^2] / [(1/2) * m * v^2]
= (9v^2) / (v^2)
= 9

Therefore, if you run three times as fast, you will have 9 times as much kinetic energy.

The correct answer is C) 9 times as much.