If the speed of a marble doubles, what does the kinetic energy do?

Answer

Dear Sam

The easiest way to answer your question is to look at the formula for the kinetic energy. The kinetic energy is equal to the mass of the marble times its velocity squared, divided by two:

E = 1/2*m*v².

The speed of the marble doubles, this means that v becomes 2*v. So if we replace v by 2*v in the formula, we get:

E = 1/2*m*(2*v)²

We can also write that as:

E = 1/2*m*2²*v²

And further:

E = 1/2*m*4*v² = 4*(1/2*m*v²), which is 4 times the original kinetic energy.

This is also clear from an example. If we take a marble of 3 grams (0.003 kg) that moves at 2 m/s, we have a kinetic energy of 0.003*2²/2 = 0.006 J (Joule) . If we double the speed to 4 m/s, then the kinetic energy is 0.003*4²/2 = 0.024 J, so indeed 4 times as great.

In general you can say that if you multiply the speed by a factor a, the kinetic energy increases by a factor a²:

E = 1/2*m*(a*v)² = a²*(1/2*m*v²).

Kind regards

Henri