What is (i) Motion in a Straight Line Frame of references, Motion in a straight line (one dimension): Position-time graph, speed and velocity. Elementary concepts of differentiation and integration for describing motion, uniform and non- uniform motion, average speed, velocity, average velocity, instantaneous velocity and uniformly accelerated motion, velocity - time and position - time graphs. Relations for uniformly accelerated motion (graphical treatment).
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A frame of reference is a coordinate system that allows us to describe the position and motion of objects. For motion in a straight line, we establish a single axis with an origin point and define a positive direction. The position of any object can then be described by a single coordinate value along this axis.
A position-time graph is a fundamental tool in physics that shows how an object's position changes over time. The slope of this graph represents the object's velocity. A horizontal line indicates the object is at rest, a straight sloped line shows uniform velocity, and a curved line represents non-uniform velocity or acceleration.
Speed is a scalar quantity representing the rate of covering distance, while velocity is a vector quantity representing the rate of change of position. Using calculus, instantaneous velocity is the derivative of position with respect to time, and acceleration is the derivative of velocity. The slope of a position-time graph at any point gives the instantaneous velocity at that moment.
Motion can be classified as uniform or non-uniform. Uniform motion occurs when an object moves with constant velocity, covering equal distances in equal time intervals with zero acceleration. Non-uniform motion involves changing velocity, where the object covers unequal distances in equal time intervals due to non-zero acceleration. The position-time graphs clearly show these differences.
For uniformly accelerated motion, we have four fundamental kinematic equations. These relate initial velocity, final velocity, acceleration, displacement, and time. The velocity-time graph for uniform acceleration is a straight line, where the slope represents acceleration and the area under the curve represents displacement. These equations are essential tools for solving motion problems in physics.