STATEMENT-1 For an observer looking out through the window of a fast moving train, the nearby objects appear to move in the opposite direction to the train, while the distant objects appear to be stationary. and STATEMENT-2 If the observer and the object are moving at velocities \(\vec{V}_{1}\) and \(\vec{V}_{2}\) respectively with reference to a laboratory frame, the velocity of the object with respect to the observer is \(\vec{V}_{2}-\vec{V}_{1}\). (A) STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT- 2 is a correct explanation for STATEMENT-1 (B) STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is NOT a correct explanation for STATEMENT-1 (C) STATEMENT-1 is True, STATEMENT- 2 is False (D) STATEMENT-1 is False, STATEMENT-2 is True

Relative velocity is the measure of the velocity of an object as seen by an observer in a different frame of reference. In simpler terms, if you're watching a car drive by while standing on the sidewalk, the car's velocity relative to you is different than it would be to someone sitting inside it. When two objects are moving with velocities \(\vec{V}_{1}\) and \(\vec{V}_{2}\) in the same frame of reference, the relative velocity of one object as observed from the other is \(\vec{V}_{2} - \vec{V}_{1}\).

In physics problems, especially in the JEE Advanced exams, the calculation of relative velocity is crucial because it helps in solving questions related to the motion of objects within different reference frames. Understanding this concept ensures that students can easily tackle problems where multiple objects are in motion and predicts the outcomes of their interactions. For example, when two trains move towards each other on parallel tracks, the concept of relative velocity will help in determining the velocity of one train as seen by an observer in the other train.

A frame of reference is like a stage on which physics takes place. In kinetic scenarios, where objects and observers are in motion, choosing the correct frame of reference can either simplify the problem or make it considerably more complex. The frame of reference serves as the 'laboratory frame' that to which all movement is compared.

One can think of it as a viewpoint from which measurements of positions, velocities, and accelerations are made. In most physics problems, there is often an implicit choice of a frame of reference, which is generally considered to be stationary or inertial, meaning it's not accelerating. When solving problems in JEE Advanced physics or any kinematics-focused topics, identifying and understanding the appropriate frame is critical. For instance, an observer inside a moving bus has a different frame of reference compared to someone standing on the street as their states of motion are not the same.

The Joint Entrance Examination (JEE) Advanced is a highly competitive test aspiring engineers in India take to gain entry into prestigious institutes like the IITs. One of its core subjects is physics, with a significant emphasis on understanding and applying core concepts like motion, forces, and energy in complex problem-solving situations.

JEE Advanced physics problems, such as those involving relative velocity and frame of reference, demand a deep conceptual understanding as well as analytical skills to approach and solve them correctly. The exam's physics section tests a student's ability to interpret physical situations and apply mathematical models to get the right solution, much like the relative motion situation provided in our example.

Motion perception refers to the process of interpreting sensory information to understand the movement of objects within our environment. It involves a complex interplay between the eyes, brain, and often other sensory information, to create a cohesive picture of what's happening. As observed from the moving train, closer objects seem to move fast in the opposite direction, while distant ones appear stationary.

This phenomenon is due to the way our brain processes visual information; it's easier to detect changes in position for objects that are near. On a broader look, motion perception is a principle found not only in physics but also heavily studied in fields like psychology and neuroscience. Understanding how we perceive motion is essential not only for solving physics problems but also for applications like improving the safety of vehicle navigation systems or understanding sensory disorders.