04PositionVelocityAcceleration

04PositionVelocityAcceleration - ● demo#0 toss ball into...

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if v is constant displacement change in position area under v(t) workbook: 2.2b page 2-3 s = v s t 04 position, velocity and acceleration
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displacement when v isn't constant integral = area under curve between curve and axis s f = s i t i t f v s t dt
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integrating equations power laws polynomials example: for now, A and V 0 are just constants t 0 t 1 At n dt = [ At n 1 n 1 ] t 0 t 1 = At 1 n 1 n 1 At 0 n 1 n 1 f t  g t  dt = f t dt g t dt v t = At V 0 x t = 0 t v t ' dt ' = 0 t At ' V 0 dt ' x t = [ 1 2 At ' 2 V 0 t ' ] 0 t = 1 2 At 2 V 0 t
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example: x 2 = x 0  0 2 − 4 6 t 2 dt x 2 =− 2 [ 4 t 2 t 3 ] 0 2 x 2 =− 2 [− 4  3  2  2 3 ]− 0 x 2 = 6 x t = x 0  0 t − 4 6 t 2 dt x t =− 2 4 t 2 t 3 v t =− 4 6 t 2 x 0 =− 2
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exercise assume x(0)=0 m what's x(t) for t =... 1s? 2s? 3s? 4s? 5s? (A) 5m (B) 10m (C) 20m (D) 45 m (E) something else can you sketch a graph of x(t)? follow up: workbook problem 2.17 , page 2-10
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acceleration
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Unformatted text preview: ● demo #0: toss ball into air – positive y upwards ● is the velocity (A) positive (B) negative (C) zero – on the way up? at the top? on the way down? ● what about the acceleration? ● demo #1: roll ball down a gentle incline – how does velocity change with time? – what does this say about acceleration? ● demo #2: roll ball up a gentle incline – same questions. .. what's going on at turning point? a avg ≡ v t a ≡ dv dt motion graphs “gravity” ● gravity is a force (more later) ● g = + 9.8 m/s 2 – g>0; a y = - g – this is the acceleration of gravity near earth's surface ● inclined planes: ● ● limiting cases – q = 0º ● no acceleration – q = 90º ● free fall a ∥ = g sin...
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