Question

Assertion:
The kinetic energy, with any reference, must be positive.
Reason:
In the expression for kinetic energy, the velocity appears with power 2.
(A) Both assertion and reason are CORRECT and the reason is the CORRECT explanation of the assertion.
(B) Both assertion and reason are CORRECT, but reason is NOT THE CORRECT explanation of the assertion.
(C) Assertion is CORRECT, but reason is INCORRECT.
(D) Assertion is INCORRECT, but reason is CORRECT.

Answer 1

Hint: To answer this question we should be knowing the formula of kinetic energy at first. From the formula we have to check the sign that can be assigned to the quantities which combine to form the formula of kinetic energy. Every physical quantity has its own way of representation.

Complete step by step answer:
We know that the kinetic energy of a body is represented as $K={\displaystyle \frac{1}{2}}m{v}^2$.
Here m represents the mass of the body that is taken into consideration and v is the velocity of the body.
Now it is known to us that mass of a body is defined as the inertia of the body or the resistance that the body will show under a situation which demands a change in its motion. Hence we can say that the mass of the body cannot be negative in nature.
So the only quantity in the formula of kinetic energy that is left out is the velocity. So it is the velocity that has to be positive or negative. But in the formula, as we can see that the velocity is in the square form.
It is known to us that the square of a positive as well as negative quantity is always positive. Hence the value of velocity is positive.
So we can say that kinetic energy is always positive.
Therefore, both assertion and reason are CORRECT and the reason is the CORRECT explanation of the assertion.

Hence option A is correct.

Note: Kinetic energy is defined as the energy that is present in a body when the body is in motion. It should be known to us that when a body acquires rest from a state of motion, the entire kinetic energy present in the body changes to the potential energy.