Question

Which statement best compares momentum and kinetic energy? If you double the velocity of an object, its kinetic energy doubles. But for the same increase in velocity, the momentum increases four times. If you double the velocity of an object, its momentum doubles. But for the same increase in velocity, the kinetic energy increases four times. If you double the velocity of an object, its momentum and kinetic energy doubles. If you double the velocity of an object, its momentum and kinetic energy increases four times.

Answer 1

If you double the velocity of an object, its momentum doubles. but for the same increase in velocity, the kinetic energy increases 4 times..

Answer 2

If you double the velocity of an object, its momentum doubles. But for the same increase in velocity, the kinetic energy increases four times.

Explanation:

We can prove this statement by looking at the formulas for the momentum and kinetic energy of an object.

Momentum: $p=mv$

Kinetic energy: $K=\frac{1}{2}mv^2$

where m is the mass of the object and v its velocity.

From the two formulas, we see that the momentum is directly proportional to the velocity, while the kinetic energy is proportional to the square of the velocity. Therefore, if we double the velocity, the momentum increases by a factor 2, while the kinetic energy increases by a factor $2^2=4$.