Physics131_L03WI10

Physics131_L03WI10 - Physics 131 - Mechanics Le cture3 one...

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Physics 131 - Mechanics Lecture 3 one dimensional Motion January 8, 2010 Homeyra Sadaghiani
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October 24, 2010 Physics 131 - Lecture 3 2 Announcements Class introduction is due Sunday January 10 th by midnight. The first Preflight 1 was a Practice No Class on Monday Jan 11 th ! The tutorial assignment is due in class on
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Week Date L# Lecture topic Text reading HW 1 4-Jan 1 Description of course structure, SI units 6-Jan 2 Motion, position, velocity, acceleration 1.1-8 (26 P) HW#0 8-Jan 3 One-dimensional motion 2 11-Jan F1 Furlough (Constant acceleration -Tutorial)   13-Jan 4 Vectors HW#1   15-Jan 5 Constant acceleration   3   20-Jan 6 Two- dimensional motion 4.1-3 (12 P) HW#2   22-Jan 7 Circular and relative motion 4.3-7 (14 P) 4 25-Jan 8 Force, mass, inertial frames 5.1-4 (11 P)   27-Jan 9 Newton’s first & second Law 5.5-7 (8 P) HW#3 29-Jan E1 EXAM 1- Chapters 1-4 October 24, 2010 Physics 131 - Lecture 3 3 Lecture Schedule We are here!
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October 24, 2010 Physics 131 - Lecture 3 4 The graph shows how the position x of a particle depends on time t . Which choice is closest to the average speed of the particle in the time interval between 0 and 6 s? A. 0.40 m/s B. 0.67 m/s C. 0.75 m/s D. 1.50 m/s E. 2.22 m/s Clicker Question 1
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October 24, 2010 Physics 131 - Lecture 3 5 Example: A Stone Dropped from a Cliff The position x of a stone dropped from a cliff is described approximately by the equation x = 5t 2 , where x is in meters and t is in seconds. The +x direction is downward and the origin is at the top of a cliff. Find the velocity of the stone during its fall as a function of time.
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October 24, 2010 Physics 131 - Lecture 3 6 Example: A Stone Dropped from a Cliff The position x of a stone dropped from a cliff is described approximately by the equation x = 5t 2 , where x is in meters and t is in seconds. The +x direction is downward and the origin is at the top of a cliff. Find the velocity of the stone during its fall as a function of time. By definition, instantaneous velocity is: 2 0 0 ( ) ( ) ( ) lim lim with ( ) 5 x t t x x t t x t v t x t t t t ∆ → ∆ → + - = = = 2 2 2 ( ) 5( ) 5 10 5 x t t t t t t t t + = + = + ∆ + 2 2 2 2 ( ) ( ) (5 10 5 ) 5 10 5 x x t t x t t t t t t t t t = + - = + ∆ + - = ∆ + 2 0 0 0 10 5 ( ) lim lim lim10 5 10 x t t t x t t t v t t t t t t ∆ → ∆ → ∆ → ∆ + = = = + ∆ = ( ) 10 x v t t =
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October 24, 2010 Physics 131 - Lecture 3 7 Differentiation and Velocity 0 ( ) lim x t x dx v t t dt ∆ → = 1 ( ) If ( ) , then ( ) n n n x dx d C t x t C t v t Cnt dt dt - = = = = 2 2 2 1 (5 ) If ( ) 5 , then ( ) (5 2) 10 x dx d t x t t v t t t dt dt - = = = = × = Instead of taking limits every time, we can simply differentiate the expression for the position x with respect to time t to obtain the instantaneous velocity v x = dx/dt .
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October 24, 2010 Physics 131 - Lecture 3 8 Example: A Train-Hopping Bird Two trains 60 km apart approach each other on parallel tracks, each train moving at 15 km/hr. A bird flies back and forth between the trains at 20 km/hr, until the trains pass each other. How far does the bird fly?
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Physics131_L03WI10 - Physics 131 - Mechanics Le cture3 one...

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