Detailed video on Relative motion in 1 dimension. Including 5 JEE ADVANCED type questions

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Welcome to our detailed study of relative motion in one dimension. Motion is always relative to a reference frame. The same motion appears different when observed from different reference frames. Consider a person walking inside a moving train. From the ground observer's perspective, both the train and person are moving. But from the train's reference frame, only the person appears to be moving. The basic formula for relative velocity is v_AB equals v_A minus v_B, where v_AB represents the velocity of object A relative to object B. Now let's develop the complete mathematical framework for one-dimensional relative motion. The position relationship is x_AB of t equals x_A of t minus x_B of t. Similarly, relative velocity is v_AB equals v_A minus v_B, and relative acceleration is a_AB equals a_A minus a_B. These graphs show position versus time for two objects A and B, along with their relative position. The slopes of these lines represent their velocities. Object A moves at 0.5 meters per second, object B at 0.3 meters per second, giving a relative velocity of 0.2 meters per second. Sign conventions and coordinate systems are crucial for obtaining correct solutions. Let's develop a systematic approach to solving relative motion problems. First, identify all reference frames involved. Second, set up a consistent coordinate system. Third, apply the relative motion equations we derived. Fourth, use graphical analysis when helpful. Common problem types include meeting problems where objects approach each other, overtaking scenarios where faster objects catch up to slower ones, and problems involving acceleration. Here we see two cars approaching each other with velocities of 20 and 15 meters per second respectively. Their relative velocity is 35 meters per second. This systematic approach helps tackle even complex JEE Advanced problems efficiently. Let's solve our first JEE Advanced problem. Two trains approach each other. Train A moves at 72 kilometers per hour, Train B at 54 kilometers per hour. They are initially 500 meters apart. We need to find the time and position where they meet. First, convert units: Train A moves at 20 meters per second, Train B at 15 meters per second. Since they approach each other, relative velocity is 20 plus 15 equals 35 meters per second. Time to meet is distance divided by relative velocity: 500 divided by 35 equals 14.3 seconds. The meeting position is 20 times 14.3 equals 286 meters from Train A's starting point. This systematic approach ensures accurate solutions. Now let's tackle more advanced problems involving variable acceleration. Problem 3 deals with objects having quadratic position functions. Object A has position x_A equals 2t squared plus 3t, while object B has position x_B equals t squared plus 5t plus 10. To find relative motion, we subtract: x_rel equals t squared minus 2t minus 10. Taking the derivative gives relative velocity: v_rel equals 2t minus 2. The second derivative gives constant relative acceleration of 2 meters per second squared. The objects meet when x_rel equals zero, which occurs at t equals 1 plus or minus square root of 11. This calculus-based approach is essential for complex JEE Advanced problems involving non-uniform motion.