Lecture-03-08[1]

# Lecture-03-08[1] - Kinematics Kinematics Kinematics...

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1 Kinematics Kinematics ± Kinematics: Description of Motion ± position and displacement ± velocity ± average ± instantaneous ± acceleration ± average ± instantaneous 10

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2 Displacement, Velocity and Speed Displacement i x x x f Δ Average velocity x x x v i x f Δ = dt dx t x v x = Δ Δ = lim t t t i f Δ Average speed Spent Time Total Traveled Distance Total v Instantaneous velocity Instantaneous speed dt dx t x v x = Δ Δ = 0 Δt Stop-Motion Photography We can superimpose all the frames to create a “stop-motion” picture that shows the progression of positions as equal intervals of time pass. 4 The equal spacing of the images indicates that the car has a constant velocity .
3 Change and Motion A stationary ball on the ground. Same position at all times. Velocity=0. A skateboarder rolling on a sidewalk. Images are equally spaced. Velocity=consta A sprinter starting the 100 meter dash. 5 Image spacing grows. Velocity increasing. A car stopping for a red light. Image spacing shrinks. Velocity decreasing. The actual images can be replaced by “dots” showing successive positions. Motion Diagrams 6

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4 Position & Displacement A student on a bicycle is moving in a straight line. The coordinate axis consists of a line along the path of the bicycle. A point on this line chosen as the origin O . Other points are assigned a number x , the value of x being proportional to the distance from O . The numbers assigned to points to the right of O are positive, as shown, and those assigned to points to the left of O are negative. When the bicycle travels from point x i to point x f , its displacement is: Δ x = x f x i . Interpreting a Position Graph Motion of a car 8
5 Average Speed & Velocity Average speed (scalar) total distance total time s t ≡= Δ av x Average velocity (vector) fi xx x v Δ ≡≡ = GG G G av x (so ) ttt xv t Δ− Δ= Δ Instantaneous Velocity & Speed 0 ( ) lim slope of line tangent to vs. curve.

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Lecture-03-08[1] - Kinematics Kinematics Kinematics...

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