Question

If the speed of a particle is doubled, what happens to its kinetic energy?
A. It becomes four times larger.
B. It becomes two times larger.
C. It becomes $\sqrt 2 $ times larger
D. It becomes unchanged
E. It becomes half as large

Answer 1

Hint:The kinetic energy of an item is the energy it has owing to its motion in physics. It is the amount of effort required to propel a body of a given mass from rest to a certain velocity. The body retains its kinetic energy after gaining it during acceleration unless its speed changes. When the body decelerates from its current speed to a condition of rest, it does the same amount of effort.

Complete step by step answer:
The kinetic energy of a point object (an item so tiny that its mass may be considered to exist at one place) or a non-rotating rigid body is determined by its mass as well as its speed in classical mechanics. The kinetic energy is equal to half of the product of mass and speed squared. In formula form: where m is the mass of the body and v is its speed (or velocity).Mass is measured in kilogrammes, speed in metres per second, and kinetic energy is measured in joules in SI units.
\[{E_{\text{k}}} = \dfrac{1}{2}m{v^2}\]

As a result, kinetic energy is proportional to the mass of the item and the square of the body's speed.If the particle's speed is twice, the kinetic energy is multiplied by four.
${\text{K}}{{\text{E}}_1} = \dfrac{1}{2}{\text{mv}}_1^2$
$\Rightarrow {\text{K}}{{\text{E}}_2} = \dfrac{1}{2}{\text{m}}{{\text{v}}_2}^2$
Where ${{\text{v}}_2} = 2{{\text{v}}_1}$. Substituting the value of ${v_2}$ in the formula,
${\text{K}}{{\text{E}}_2} = \dfrac{1}{2}\;{\text{m}}{\left( {2{{\text{v}}_1}} \right)^2}$
$\Rightarrow {\text{K}}{{\text{E}}_2} = \dfrac{1}{2}\left( {4{\text{mv}}_1^2} \right)$
$\therefore {\text{K}}{{\text{E}}_2} = 4{\text{K}}{{\text{E}}_1}$

Hence option A is correct.

Note:Because kinetic energy is proportional to the square of speed, an item that doubles its speed has four times the kinetic energy. For example, assuming constant braking power, a car going twice as fast as another takes four times the distance to stop. As a result of this quadrupling, doubling the speed requires four times the effort.