PreExam1Review

PreExam1Review - Very very important Pre-requisites: c...

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Very very important Pre-requisites: Trigonometry : Basic definitions: sin θ =? cos θ =? tg θ =? Algebra: quadratic equation If ax 2 +bx+c=0, x=? Linear Equations of multiple variables: y=k 1 x+b 1 , y=k 2 x+b 2 (slope and x,y intercept) Calculus: Basic derivatives and integrals: a b c θ dx N dx = Nx N 1 de x dx = e x d sin x dx = cos x d cos x dx = sin x Chain rules:
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Summary of Chapter 2 (concepts) Under stand the basic laws of motions along a straight line Be able to interpret and draw x-t and v-t graphs Derive velocity, acceleration from x-t Derive acceleration, displacement from v-t What is a free fall:Constant acceleration due to gravity Be able to graphically demonstrate what is velocity on a x-t graph, what is acceleration, as well as displacement, on an v-t graph. Understand the mathematical relation between x, v,t, a, when a is not constant Differentiate instantaneous and average velocity/acceleration
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Summary (CH1 and CH2 equations) Vectors decomposition Vector addition 1d motion (constant acceleration) V = V x ˆ i + V y ˆ j = | V | cos θ ˆ i + | V | sin ˆ j V tot = ( V 1 x + V 2 x ) ˆ i + ( V 1 y + V 2 y ) ˆ j tg = V 1 y + V 2 y V 1 x + V 2 x | V tot | = V 1 x + V 2 x ) 2 + ( V 1 y + V 2 y ) 2 v avg = Δ x/ Δ t = (x-x 0 )/(t-t 0 ) a avg = Δ v/ Δ t = (v x -v 0x )/(t-t 0 ) v x = v 0 x + a x t x = x 0 + v 0 x t + 1 2 a x t 2 v x 2 = v 0 x 2 + 2 a x ( x x 0 ) x x 0 = 1 2 ( v x + v x 0 ) t Average velocity/acceleration Instantaneous velocity/acceleration v x = dx dt a x = dv x dt
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Example: (Austin Powers VS Dr. Evil) A helicopter carrying Dr. Evil takes off with a constant upward acceleration of 5.0m/s2. Secret agent Austin Powers jumps on just as the helicopter lifts off the
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PreExam1Review - Very very important Pre-requisites: c...

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