Review Sheet _2_1

Review Sheet _2_1 - x-direction and in the y-direction...

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Rev. 2 REVIEW SHEET #2: Linear Motion Definitions of kinematic quantities: Position vector relative to origin ˆ ˆ ˆ r xi yj zk = + + r Displacement (vector) 2 1 ˆ ˆ ˆ r r r xi y j z k ∆ = - = ∆ + ∆ + ∆ r r r Velocity (vector) 2 1 2 1 ˆ ˆ ˆ ave r r r x y z v i j k t t t t t t - = = = + + - r r r r ˆ ˆ ˆ ˆ ˆ ˆ inst x y z dr dx dy dz v i j k v i v j v k dt dt dt dt = = + + = + + r r Acceleration (vector) 2 1 2 1 ˆ ˆ ˆ y x z ave v v v v v v a i j k t t t t t t - = = = + + - r r r r ˆ ˆ ˆ ˆ ˆ ˆ y x z inst x y z dv dv dv dv a i j k a i a j a k dt dt dt dt = = + + = + + r r Equations of Linear Motion in 1-D for Constant Linear Acceleration: Equ. (2-11): v x = v 0x + a x t Equ. (2-15): x - x 0 = v 0x t + ½a x t 2 Equ. (2-16): v x 2 = v 0x 2 + 2a x (x – x 0 ) Equ. (2-17): x - x 0 = ½(v 0x + v x )t Equ. (2-18) x - x 0 = v x t - ½a x t 2 x 0 , v 0x , and a x are constants. Note that Equ. (1) is the time derivative of Equ. (2). For linear motion in 2-D (e.g., projectile motion), you can treat the motions in the
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Unformatted text preview: x-direction and in the y-direction separately except that the time variable is the same for both motions. In problems involving projectile motion near the surface of the earth the acceleration in the y-direction is usually g=9.80 m/s 2 in the downward direction and the acceleration in the x-direction is usually zero because effects of air drag are ignored. At the highest point of its trajectory the vertical velocity component of a projectile is zero at the instant the projectile reverses its direction from going up to coming down. Phys 0174 Fall 2008 P. Koehler...
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This note was uploaded on 09/11/2011 for the course PHYS 0174 taught by Professor Kohler during the Spring '08 term at Pittsburgh.

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