Question

Kinetic energy is proportional to_____________.
THIS QUESTION HAS MULTIPLE CORRECT OPTIONS
A. Velocity
B. mass
C. square of the velocity
D. acceleration

Answer 1

Hint: We know that the kinetic energy of an object is the energy that it possesses due to its motion. To find the relation of kinetic energy with the terms given in option, use the expression of kinetic energy.

Complete step by step answer:
In this question, we have to show the relation of kinetic energy with terms given in options.
Kinetic energy is the energy associated with the movement or motion of objects.
The expression of kinetic energy is given as follows,
$K.E.=\dfrac{1}{2}m{{v}^{2}}$
Where,
m is mass
v is velocity
$\dfrac{1}{2}$ is the constant term. So we can write as
$K.E\alpha m$ and $K.E.\alpha {{v}^{2}}$
Although there are many forms of kinetic energy present, this type of energy is often associated with the movement of larger objects. Consider an example, thermal energy exists because of the movement of atoms or molecules, thus thermal energy is a variation of kinetic energy. However, kinetic energy refers to the energy associated with the movement of larger objects (most of the time). Therefore, if an object is not moving or not in motion, it is said to have zero kinetic energy. The kinetic energy of an object depends on both its mass and square velocity.
Hence, Kinetic energy is proportional to mass and square of velocity.

Therefore the correct option is an option (B) and (C).

Note:
Velocity term in kinetic energy plays a much greater role. In quantum mechanics, kinetic energy depends on the square of momentum and this is where the product term comes from. In relativity, kinetic energy is integral of v with respect to momentum and this is where the product term comes from.