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# chapter2.key - Displacement vs position Chapter 2...

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Chapter 2: One-Dimensional Motion Motion at fixed velocity Definition of average velocity Motion with fixed acceleration Graphical representations 1 Displacement vs. position Position: x (relative to origin) Displacement: ! x = x f -x i 2 basicformula v = ! x ! t = x f " x i t Average velocity Average velocity Can be positive or negative Depends only on initial/final positions e.g., if you return to original position, average velocity is zero 3 basic formula v = ! x ! t = x f " x i t Instantaneous velocity Let time interval approach zero Defined for every instance in time Equals average velocity if v = constant SPEED is absolute value of velocity 4 Graphical Representation of Average Velocity Between A and D , v is slope of blue line 5 Graphical Representation of Instantaneous Velocity v(t=3.0) is slope of tangent (green line) 6

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Example 2.1 Carol starts at a position x(t=0) = 1.5 m. At t=2.0 s, Carol’s position is x(t=2 s)=4.5 m At t=4.0 s, Carol’s position is x(t=4 s)=-2.5 m a) What is Carol’s average velocity between t=0 and t=2 s? b) What is Carol’s average velocity between t=2 and t=4 s? c) What is Carol’s average velocity between t=0 and t=4 s? a) 1.5 m/s b) -3.5 m/s c) -1.0 m/s 7 Example 2.2 On a mission to rid Spartan Stadium of vermin, an archer shoots an arrow across the stadium at an unlucky rat 200 meters away. The archer hears the squeal 2.2 seconds later. What was the velocity of the arrow? The speed of sound is 330 m/s. 8 Example 2.2: Visualize the problem! 9 Example 2.2 On a mission to rid Spartan Stadium of vermin, an archer shoots an arrow across the stadium at an unlucky rat 200 meters away. The archer hears the squeal 2.2 seconds later. What was the velocity of the arrow? The speed of sound is 330 m/s. V = 125 m/s 10 Example 2.3a The instantaneous velocity is zero at ___ A) a B) b & d C) c & e 11 Example 2.3b The instantaneous velocity is negative at _____ A) a B) b C) c D) d E) e 12
Example 2.3c The average velocity is zero in the interval _____ A) a-c B) b-d C) c-d D) c-e E) d-e 13 Example 2.3d The average velocity is negative in the interval(s) _________ A) a-b B) a-c C) c-e D) d-e 14 SPEED Speed is |v| and is always positive Average speed is sum over | ! x| elements divided by elapsed time 15 Example 2.4 2 4 6 8 2 4 6 8 10 12 0 0 A B C D E a) What is the average velocity between B and E?

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## This note was uploaded on 07/25/2008 for the course PHY 231C taught by Professor Pratt during the Spring '06 term at Michigan State University.

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chapter2.key - Displacement vs position Chapter 2...

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