Question

1. when the speed of an object is doubled (a) its kinetic energy is doubled (b) its potential energy is doubled (c) its rest energy doubled (d) its momentum is doubled (e) none of the above

Explanation:

Step1: Recall kinetic - energy formula

The kinetic - energy formula is $K = \frac{1}{2}mv^{2}$. If the speed $v$ is doubled to $2v$, the new kinetic energy $K'=\frac{1}{2}m(2v)^{2}=4\times\frac{1}{2}mv^{2}=4K$. So, kinetic energy is quadrupled, not doubled.

Step2: Recall potential - energy concept

Potential energy depends on the position of the object (e.g., $U = mgh$ for gravitational potential energy) and is not directly related to the speed of the object. So, doubling the speed does not double the potential energy.

Step3: Recall rest - energy formula

The rest - energy of an object is given by $E_{0}=mc^{2}$, which is a constant for a given object and does not depend on the speed of the object. So, rest energy is not affected by the speed change.

Step4: Recall momentum formula

The momentum of an object is $p = mv$. If the speed $v$ is doubled to $2v$, the new momentum $p'=m(2v) = 2mv=2p$. So, the momentum is doubled.

Answer:

d. its momentum is doubled