inst_07.1 - Class 7.1 Analysis of Motion & Newtons Laws...

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1 Class 7.1 Analysis of Motion & Newton’s Laws
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2 Class Objective Learn and apply Newton’s First, Second, and Third Laws Unidirectional Multidirectional Learn the relationship between position, velocity, and acceleration
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3 RAT 1
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4 Some Definitions (1D) Position - location on a straight line -3 -2 -1 0 1 2 3 4 Displacement - change in location on a straight line -3 -2 -1 0 1 2 3 4 x x x = x 2 - x 1 = 4 - (-2) = 6
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5 Some Definitions (1D) Average Velocity - rate of position change with time (vector) Time Elapsed nt Displaceme t x v ave = = dt dx t x t v = = 0 lim Instantaneous Velocity (vector) same direction, different value Speed is magnitude of the velocity.
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6 Average and Instantaneous Velocity (1D) Position Time t 1 t 2 x 1 x 2 Slope = = Average Velocity x 2 - x 1 t 2 - t 1
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7 Some Definitions (2D) Position -- a location usually described by a graphic on a map or by a coordinate system 5 4 3 2 1 -3 -2 -1 4 3 2 1 0 -1 -2 -3 -4 (-2, -3) (4, 3)
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8 Some Definitions (2D) Displacement -- change in position, where r r 4 -2 -3 -3 -4 (-2, -3) (4, 3) 5 1 r r ρ ρ 2 r r ρ r = r r 2 - r r 1
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9 Some Definitions (2D) Average velocity (vector) Instantaneous velocity (vector) Speed - the magnitude of instantaneous velocity (scalar) ( 29 ( 29 scalar Time Elapsed vector nt Displaceme t r v ave = D D = r r dt r d t r t v r r r = = 0 lim v speed r =
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10 Some Definitions (1D) Average Acceleration - rate of velocity change with time (vector) t v t t v v a 1 2 ave = - - = 1 2 Instantaneous Acceleration (vector) a = λ ιμ ∆τ→ 0 ∆ω ∆τ = δω δτ
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11 Average and Instantaneous Acceleration (1D) Velocity Time t 1 t 2 v 1 v 2 Slope = = Average Acceleration v 2 - v 1 t 2 - t 1
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12 Some Definitions (2D) Average Acceleration (vector) Instantaneous Acceleration (vector) t v t t v v a 1 2 ave = - - = r r r r 1 2 r a = λ ιμ ∆τ→ 0 ρ ω ∆τ = δ ρ ω δτ
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13 Paired Exercise 1 What is the distance traveled? What is the acceleration at 1.25 hours? Speed, miles per hour 3 2 1 0 0 10 20 Time, hours
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14 For constant acceleration. ..
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inst_07.1 - Class 7.1 Analysis of Motion & Newtons Laws...

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