Chapter 3: Motion in a Straight Line – Quick Revision Notes 1. Introduction to Motion Motion occurs when an object changes its position with time. Motion along a straight path is called rectilinear motion or one-dimensional motion. 2. Basic Terms in Kinematics Position (x): Location of an object on a reference scale. Path Length: Total distance traveled by an object, always positive. Displacement (Δx): Shortest distance between initial and final positions. It is a vector quantity and can be positive, negative, or zero. 3. Distance vs. Displacement Distance is a scalar quantity and does not depend on direction. Displacement is a vector quantity and depends on the initial and final positions. 4. Speed and Velocity Speed (v): Distance traveled per unit time. It is always positive. Average Speed = Total Distance / Total Time. Velocity (v): Displacement per unit time. It is a vector quantity and can be positive, negative, or zero. Average Velocity = Total Displacement / Total Time. Instantaneous velocity is the velocity of an object at a particular instant. 5. Acceleration (a) Change in velocity per unit time. Acceleration is positive when velocity increases and negative when velocity decreases (deceleration or retardation). Average Acceleration = Change in Velocity / Time. 6. Graphical Representation of Motion Position-Time Graph (x-t Graph): A straight line represents uniform motion. A curved line represents non-uniform motion. Velocity-Time Graph (v-t Graph): The area under the v-t graph gives displacement. The slope of the v-t graph gives acceleration. Acceleration-Time Graph (a-t Graph): The area under the a-t graph gives velocity change. 7. Equations of Motion (for Uniformly Accelerated Motion) 1. v = u + at → Final velocity after time t. 2. s = ut + (1/2)at² → Displacement in time t. 3. v² = u² + 2as → Velocity after displacement s. 4. s = (u + v)t / 2 → Displacement using average velocity. Where: u = Initial velocity v = Final velocity a = Acceleration s = Displacement t = Time 8. Free Fall Motion When an object falls under gravity, it experiences acceleration due to gravity (g = 9.8 m/s²). Equations of motion remain the same, replacing a with g. For free fall: Initial velocity u = 0 if dropped from rest. Acceleration a = g = 9.8 m/s² downward. Velocity after falling for time t: v = gt. Displacement after time t: s = (1/2)gt². Velocity just before hitting the ground: v² = 2gs. 9. Relative Motion in One Dimension When two objects move in the same direction, their relative velocity is V₁ - V₂. When two objects move in opposite directions, their relative velocity is V₁ + V₂. Final Exam Tips ✔ Understand and apply motion equations correctly. ✔ Practice graphical questions for better conceptual clarity. ✔ Be careful with sign conventions (taking one direction as positive and the opposite as negative). ✔ Solve numerical problems on free fall and relative motion. This is a quick revision summary of the chapter. Join for more - https://whatsapp.com/channel/0029Va9492L3QxRv5MtNFF0Y/151