formula sheet - One Dimensional motion v = x t Average...

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One Dimensional motion Average Velocity: t x v = / Instantaneous Velocity: t x v t = / lim 0 Average acceleration: t v a = / Instantaneous acceleration: t v a t = / lim 0 For constant acceleration only t v a = / t a v v t a t v x x x x x x x + = + + = 0 2 2 1 0 0 Projectile motion gt v v v v gt t v y y t v x x y y x x y x - = = - + = + = 0 0 2 2 1 0 0 0 0 2 / 80 . 9 s m g = Newton’s Laws, Forces a m F = BA AB F F - = mg F = (Gravity) kx F - = (Spring) Work, Energy θ cos Fd W = 2 2 1 mv K = mgh U = (Gravity) 2 2 1 kx U = (Spring) Oscillations T f π π ϖ 2 2 = = ) cos( ) sin( ) cos( 2 φ ϖ ϖ φ ϖ ϖ φ ϖ + - = + - = + = t A a t A v t A x m k f π 2 1 = ; l g f π 2 1 = ; Vl a v f π 2 = Waves f T v λ λ = = μ F v = ; L m = μ (String) ( 29 s m t v / 6 . 0 3 . 331 + = (For air) ( 29 e destructiv n r r ve constructi n r r + = - = - λ λ 2 1 1 2 1 2 Strings & tubes (symmetric) ... 3 , 2 , 1 = n 1 2 2 2 nf L nv v f n L L n n n n n = = = = = λ λ λ Strings & tubes (fixed /closed at one end) 1 4 4 4 ... 5 , 3 , 1 nf L nv v f n L L n n n n n n = = = = = = λ λ λ Reflection 2 1 θ θ = Refraction 1 2 1 2 1 2 sin sin λ λ θ θ = = v
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