A particle is found to be at rest when seen from a frame ${S_1}$ and moving with a constant velocity when seen from another frame ${S_2}$. Mark out the possible option:
A) Both the frames are inertial
B) Both the frames are non-inertial
C) ${S_1}$ is inertial and ${S_2}$ is non-inertial
D) ${S_1}$ is non-inertial and ${S_2}$ is inertial.

Hint: Recall that the frame of reference is defined as the set of coordinates and they can be used to determine the positions and the velocities of different objects in different frames of reference moving with respect to each other. The frame of reference is of two types- inertial frame of reference and non inertial frame of reference.

Complete answer:
In an inertial frame of reference, Newton’s first law is obeyed. This means a particle will continue to be in its state of rest or motion until an external force is acting on it. The body does not accelerate and moves with a constant velocity. Also the force acting on the body is real.
Given that the particle is at rest when seen from the frame of reference ${S_1}$ and is moving with a constant velocity from the another frame of reference ${S_2}$.
Therefore, both the given frames are non accelerated and thus they are inertial.

Hence, Option A is the right answer.

Note: In a non inertial frame of reference, Newton’s laws are not obeyed. This means that the body can change its state of rest or motion without any external force acting on it. Also the body moves with variable velocity and has some acceleration. Since the body is accelerating in this frame of reference, so there will be some force acting in this frame. For example, if a car has started its motion from rest, then while the time it accelerates, the car will be in a non inertial frame of reference.