2D Motion - 1 Chapter 4: Chapter 4: Motion in Two...

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Unformatted text preview: 1 Chapter 4: Chapter 4: Motion in Two Dimensions Position and Displacement Position and Displacement c The position of an object is described by its position vector, r c The displacement of the object is defined as the change in its position b r = r f- r i c The average velocity is the ratio of the displacement to the time interval for the displacement b The direction of the average velocity is the direction of the displacement vector, r Average Velocity t = r v 2 Instantaneous Velocity Instantaneous Velocity c The instantaneous velocity is the limit of the average velocity as t approaches zero lim t d t dt = r r v c The direction of the instantaneous velocity vector at any point in a particles path is along a line tangent to the path at that point and in the direction of motion c The magnitude of the instantaneous velocity vector is the speed b The speed is a scalar quantity Average Acceleration Average Acceleration c The average acceleration of a particle as it moves is defined as the change in the instantaneous velocity vector divided by the time interval during which that change occurs. f i f i t t t = = v v v a c As a particle moves, v can be found in different ways c The average acceleration is a vector quantity directed along v c The instantaneous acceleration is the limit of the average acceleration as v / t approaches zero lim t d t dt = v v a Instantaneous Acceleration Instantaneous Acceleration 3 Kinematic Equations for Two Kinematic Equations for Two-Dimensional Motion Dimensional Motion c For constant acceleration, 2D equation of motion is similar to those of one-dimensional kinematics j y i x r a + = Position, Velocity: j i j i a a y x v v dt dy dt dx dt r d v + = + = = a = constant, a x and a y are also constant We can use 1D kinematic equations t a v v t a v v y yi yf x xi xf + = + = and )t j i ( ) j i ( j ) ( i ) ( a y x yi xi y yi x xi f a a v v t a v t a v v + + + = + + + = t a v v i f a a a + = 2 2 2 1 and 2 1 t a t v y y t a t v x x y yi i f x xi i f + + = + + = 2 2 2 ) j i ( 2 1 ) j i ( ) j i ( j ) 2 1 ( i ) 2 1 ( j i t a a t v v y x t a t v y t a t v x y x r y x yi xi i i y yi i x xi i f f f a + + + + + = + + + + + = + = 2 2 1 t a t v r r i i f a a a a + + = Similarly: is the vector sum of (i) the original position , (ii) displacement arising from the initial velocity (iii) and a displacement resulting from the constant acceleration f r a t v i a 2 2 1 t a a i r a 4 Kinematic Equations, Component Equations...
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This note was uploaded on 07/30/2011 for the course PHY 2048 taught by Professor Bose during the Spring '08 term at University of Central Florida.

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2D Motion - 1 Chapter 4: Chapter 4: Motion in Two...

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