Chapter03 - Chapter 3: Motion in 2D and 3D Position and...

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Physics 1301: Chapter 2, Pg 1 Chapter 3: Motion in 2D and 3D ¾ Position and displacement ¾ Velocity and speed ¾ Acceleration ¾ Trajectories ¾ Motion with constant acceleration ¾ Projectile motion ¾ Uniform circular motion ¾ Relative motion
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Physics 1301: Chapter 2, Pg 2 Position vector Position vector: ¾ = a vector connecting the origin of the coordinate system to the point of interest ¾ 2D: j i r + = ) ( ) ( ) ( ) ( ) ( 0 t y t x t y t x t z k j i r + + ) ( ) ( ) ( ) ( ) ( ) ( ) ( t z t y t x t z t y t x t
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Physics 1301: Chapter 2, Pg 3 Displacement vector Displacement vector: ¾ = change of position vector: ¾ Vector notation: + + + + + + ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( t z t y t x t z t t z t y t t y t x t t x t z t y t x t t z t t y t t x t r ) ( ) ( ) ( t t t t r r r + k j i r + + ) ( ) ( ) ( ) ( t z t y t x t
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Physics 1301: Chapter 2, Pg 4 Average velocity Average velocity: ¾ = displacement divided by time interval ± A vector pointing from initial to final position ¾ Vector notation: ¾ 2D: t = r v k j i r v + + z y x z y x v v v v v v t z t y t x z y x t t 1 j i v + y x v v
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Physics 1301: Chapter 2, Pg 5 Distance traveled and average speed Distance traveled (path of motion) ¾ = a positive scalar equal to the length of a part of the trajectory between initial and final points Average speed: ¾ = distance traveled divided by time interval ± Speed is a positive scalar t l s r l v s Path dl l
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Physics 1301: Chapter 2, Pg 6 Velocity and speed Velocity: ¾ = time derivative of position ± A vector pointing in the direction of motion ± A tangent to the trajectory Speed: ¾ = time derivative of the distance traveled ¾ = magnitude of velocity dt d r v v dt d dt d dt dl s v r r
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