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Lect02 - Physics 112 Lecture 2 Agenda for Today 1-D...

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Physics 112: Lecture 2 Agenda for Today 1-D Kinematics 1-D Kinematics – Average & instantaneous velocity and acceleration – Motion with constant acceleration
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Motion in 1 dimension In 1-D, we usually write position as x(t). Since it’s in 1-D, all we need to indicate direction is + or . Displacement in a time Δ t = t 2 - t 1 is Δ x = x(t 2 ) - x(t 1 ) = x 2 - x 1 t x t 1 t 2 Δ x Δ t x 1 x 2 some particle’s trajectory in 1-D
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1-D kinematics t x t t ) t ( x ) t ( x v 1 2 1 2 av Δ Δ = t x t 1 t 2 Δ x x 1 x 2 trajectory • Velocity v is the “rate of change of position” Average velocity v av in the time Δ t = t 2 - t 1 is: Δ t V av = slope of line connecting x 1 and x 2 .
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Consider limit t 1 t 2 Instantaneous velocity v is defined as: 1-D kinematics... dt ) t ( dx ) t ( v = t x t 1 t 2 Δ x x 1 x 2 Δ t so v(t 2 ) = slope of line tangent to path at t 2 .
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Puzzle Yesterday I was driving down Green Street, when I was stopped by a police officer. He said to me “You were going 60 miles an hour.” I responded, “I’ve only been driving for 10 minutes! How could I possibly have gone 60 miles an hour, when I haven’t even been traveling for an hour?” What’s wrong with my argument?
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Graph of x(t) versus time, what’s the average velocity? T
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Definition of SPEED: distance traveled without regard to direction, divided by time t. What’s the average speed? Average speed average velocity!
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1-D kinematics... t v t t ) t ( v ) t ( v a 1 2 1 2 av Δ Δ = • Acceleration a is the “rate of change of velocity” Average acceleration a av in the time Δ t = t 2 - t 1 is: And instantaneous acceleration a is defined as: 2 2 dt ) t ( x d dt ) t ( dv ) t ( a = = dt ) t ( dx ) t ( v = using
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Recap If the position x
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