Question

When the mass and velocity of the body are doubled, what happens to its kinetic energy?

Answer 1

Hint: In simple word kinetic energy is energy which the body gets while the body is in motion. The energy of a body depends on mass and velocity. Kinetic energy is equal to half of the product mass and velocity. SI unit is joules.

Complete answer:
To solve the question first understand what question you want to convey.
Question explanation- If the body has a mass m and velocity v then its energy is given by formula given in equation (1). If we have twice the mass and velocity of the body then what will be its kinetic energy?
Kinetic energy- Energy gained by a body when the body is in motion and it is given by,
\[KE=\dfrac{1}{2}m{{v}^{2}}\] ----------(1)
Now let's assume that our next kinetic energy is same as that of first kinetic energy but according to our question, the mass of next energy is double than the mass of first energy and velocity of next energy is double than the velocity of first energy which is given as
 ${{m}_{1}}=2m$ and ${{v}_{1}}=2v$
So next Kinetic energy is energy by
\[K{{E}_{1}}=\dfrac{1}{2}{{m}_{1}}{{v}_{1}}^{2}\]
Now put the value of ${{m}_{1}}\And {{v}_{1}}$ in the above equation,
We get,
\[\begin{align}
  & K{{E}_{1}}=\dfrac{1}{2}(2m){{(2v)}^{2}} \\
 & K{{E}_{1}}=\dfrac{1}{2}(2m)(4{{v}^{2}}) \\
 & K{{E}_{1}}=8(\dfrac{1}{2}m{{v}^{2}}) \\
\end{align}\]
Put the value of equation one in the above equation,
We get,
\[K{{E}_{1}}=8KE\]
So from the above equation, we can conclude that double the mass and velocity then eight will be our next energy.

Note:
Your next energy does not depend on your first energy. Do not get confused between potential energy and kinetic energy. A body possesses kinetic energy when the body is in motion and a body possesses potential energy when it is at some height.