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# lecture3 - Chapter 2 Motion in One Dimension.continued 1 1...

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Chapter 2 otion in One Dimension Motion in One Dimension …continued 1

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- Motion with niform 1 D Motion with Uniform (Constant) Acceleration Average and instantaneous accelerations are the same i f i f t t v v t v a If we choose t i =0 s and rename ā =a; v = v ; v = v ; t = t then ; i 0 ; f ; f v v a 0 t 2
elocity as a function of Velocity as a function of acceleration and time o vv a t Acceleration steadily changes v 0 by an amount at se when you don’t Use when you don’t know and aren’t asked find the displacement to find the displacement 3

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isplacement as a function of Displacement as a function of velocity and time We can express the average velocity as v v 0 ubstitute into the definition of displacement 2 v average Substitute into the definition of displacement v v f o se when you don’t know and aren’t asked for the t 2 t v x average Use when you don t know and aren t asked for the acceleration 4
isplacement as a function of Displacement as a function of acceleration, velocity and time 2 o at 1 t v x Quadratic equation 2 Displacement is equal to the area under the v vs. t graph Use when you don’t now and aren’t asked to know and aren t asked to find the final velocity 5

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Fig. 2.15, p. 35 6
Solving a quadratic equation 2 cx bx a y a, b, c are all constants ac b b 4 2 a x 2 which sign you chose depends on the problem 7

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elocity as a function of Velocity as a function of acceleration and displacement Solve for t in both equations below et them equal and clear 2  o vv a t t 2 v v t v x f o average set them equal and clear v  22 2 o a x Use when you don’t know and aren’t asked for the time 8
Kinematic Equations for Uniform Acceleration  o vv a t Use when you don’t know and aren’t asked to find the displacement   1 o x vt v v t Use when you don’t know and aren’t asked for the cceleration 2 2 1 o xv t a t acceleration Use when you don’t know and aren’t asked to find the final velocity 22 2 2 o a x Use when you don’t know and aren’t asked for the time 9

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Conceptual question Q: Can the equations of kinematics be used to find the total distance traveled? Starting from rest, a car accelerates down a straight ad with constant Ans: Yes, break up the problem into parts, one with acceleration a road with constant acceleration a 1 for a time t 1, then the acceleration is changed to a for and additional time t . 2 parts, one with acceleration a 1 for the first time interval and the other with a 2 for the second time interval, noting that in the a 2 a (m/s 2 ) 2 2 second time interval, the initial velocity is the final velocity from the first time interval.
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lecture3 - Chapter 2 Motion in One Dimension.continued 1 1...

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