Question

Define kinetic energy. What happens to the kinetic energy of a body if its velocity becomes double?

Answer 1

Kinetic energy of a body is the energy possessed by virtue of its motion.
It is proportional to the square of its velocity.The energy of a body by virtue of its position is called potential energy.

Complete step by step answer:
The kinetic energy of a moving body is measured by the amount of work, which has been done in bringing the body from the rest position to its present position, or which the body can do in going from its present position to the rest position.
For the body at rest, the kinetic energy is zero.
For a body of mass m moving with initial velocity v , kinetic energy K is given by:
$K=\dfrac{1}{2}m{{v}^{2}}$
Now, if the velocity of the body is doubled, that is, $v'=2v$, then kinetic energy of the body will become:

& K'=\dfrac{1}{2}mv{{'}^{2}} \\\ & K'=\dfrac{1}{2}m{{(2v)}^{2}} \\\ & K'=\dfrac{1}{2}m4{{v}^{2}} \\\ & K'=4K \\\ \end{aligned}$$ The kinetic energy will be four times the initial kinetic energy (K). **Note:** According to the principle of Conservation of Energy, “energy can neither be created nor can be destroyed, but can only be converted from one form to another”. So, kinetic energy is not created or destroyed. Although a body at its rest position has zero kinetic energy, it has potential energy, which is converted into kinetic energy during its motion. Similarly when a moving body comes to rest, its kinetic energy is converted into potential energy, and the body stops.