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3. Kinematics

# 3. Kinematics - Kinematics Kinematics study of motion...

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Kinematics Kinematics - study of motion disregarding the forcesinvolved. 2 Kinds of Motion 1. Uniform Motion – motion along a straight path at constant speedor velocity. vt s = 2. Uniformly Accelerated Motion – motion along a straight path at constant acceleration with variable velocities. at v v + = 0 ( 29 0 2 0 2 2 x x a v v - + = 2 0 0 2 1 at t v x x + = - Note: a positive sign is affixed on the value of a if the velocity is increasing by a uniform rate and a negative sign is affixed on the value of a if the velocity decreases by a uniform rate. Displacement - a vector quantity that represents the straight-line distance between the starting and end points. Average velocity – the total displacement of an object divided by the elapsedtime. ) ( 1 2 1 2 motion line straight t x t t x x V av = - - = Graph of an object’s position as a function of time, x-t graph The path in the figure does not represent the objects path in space, rather it is straight line. It is a pictorial way to represent how the object’s position changes with time Instantaneous velocity ∆t ∆x Slope = average velocity t x

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The averagevelocity of a particle during a time interval can not tell us how fast or in what direction the particle was moving at any given time during the interval. To describe the motion in greater detail, we need to define the velocity at any specific instant of time or specific point along the path. Such velocity is called instantaneous velocity. ) ( lim 0 motion line straight dt dx t x V t = = The limit of t x as t approaches zero is called the derivative of x with respect to t is equal to dt dx . The instantaneous velocity is the limit of the averagevelocity as the time interval approaches zero. (a) (b) (c) (a & b) as the average velocity is calculated over shorter time intervals, its value approaches the instantaneous velocity. (c) in the limit 0 t the slope of the line 2 1 P P approaches the slope of the tangent to the t x - curve at point 1 P Average and Instantaneous Acceleration Average acceleration – a vector quantity whose x-component is v , the change in the x-component of velocity, divided by the time interval t ) ( 1 2 1 2 motion line straight t v t t v v a av = - - = Instantaneous Acceleration – it is the limit of the average acceleration as the time interval approaches zero.
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3. Kinematics - Kinematics Kinematics study of motion...

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