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First_Midterm_Formula_Sheet

First_Midterm_Formula_Sheet - FORMULA SHEET You may tear...

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FORMULA SHEET You may tear this sheet out of the exam — you do not have to hand it in with the rest of your exam. R x = A x + B x , R y = A y + B y , R z = A z + B z (components of ! R = ! A + ! B ) ! A = A x ˆ i + A y ˆ j + A z ˆ k , ! B = B x ˆ i + B y ˆ j + B z ˆ k ! ! cos cos B A B A ! ! ! ! = = " AB (definition of the scalar (dot) product) z z y y x x B A B A B A + + = ! B A ! ! (scalar (dot) product in terms of components) C = AB sin ! (magnitude of ! C = ! A ! ! B ) C x = A y B z ! A z B y C y = A z B x ! A x B z C z = A x B y ! A y B x (components of ! C = ! A ! ! B ) t x t t x x v x ! ! = " " = " 1 2 1 2 av (average velocity, straight-line motion) dt dx t x v t x = ! ! = " ! 0 lim (instantaneous velocity, straight-line motion) t v t t v v a x x x x ! ! = " " = " 1 2 1 2 av (average acceleration, straight-line motion) dt dv t v a x x t x = ! ! = " ! 0 lim (instantaneous acceleration, straight-line motion) t a v v x x x + = 0 (constant acceleration only) 2 0 0 2 1 t a t v x x x x + + = (constant acceleration only) ) ( 2 0 2 0 2 x x a v v x x x ! + = (constant acceleration only) t v v x x x x ! " # $ % & + = 2 0 0 (constant acceleration only) dt a v v t x x x ! + = 0 0 ! + = t x dt v x x 0 0 k j i r ˆ ˆ ˆ z y x + + = ! t t t ! ! = " " = r r r v ! ! ! ! 1 2 1 2 av (average velocity vector) dt d t t r r v ! ! ! = = ! " " " 0 lim (instantaneous velocity vector) dt dx v x = dt dy v y = dt dz v z = (components of instantaneous velocity) t t t ! ! = " " = v v v a ! ! ! ! 1 2 1 2 av (average acceleration vector)
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