If our speed increases three times, our kinetic energy increases by a factor of nine, that is, our kinetic energy increases nine times.

The kinetic energy is a form, of mechanical energy and it is associated with the movement of the bodies. All body with mass m, which moves with a speed v, has associated a kinetic energy given by the following expression:

Ek = (mv^2)/2

Where:

m, is the mass of the body.

v, is the velocity of the body.

The kinetic energy Ek1, for the initial velocity v1 is:

Ek1 = (mv1^2)/2

As we see, the kinetic energy is proportional to the square of the speed. If the initial speed v1 increased three times, the final speed v2, will be:

v2 = 3v1

Then the kinetic energy Ek2, for the speed v2, will be:

Ek2 = (mv2^2)/2 = [m(3v1)^2]/2

Ek2 = 9(mv1^2)/2 = 9(Ek1)

So, when the speed increases three times, the kinetic energy increases nine times.

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