Chapter 2Motion Along a LineSlide 3Slide 4Slide 5Position & DisplacementSlide 7Slide 8Slide 9Slide 10Slide 11Slide 12Velocity: Rate of Change of PositionSlide 14Slide 15Slide 16Slide 17Slide 18Slide 19Slide 20Acceleration: Rate of Change of VelocitySlide 22Motion Along a Line With Constant AccelerationA Modified Set of EquationsVisualizing Motion Along a Line with Constant AccelerationSlide 26Free FallSlide 28Slide 29Slide 30Slide 31Slide 32SummaryChapter 2Motion Along a LineMFMcGraw- PHY 1410 Ch_02b-Revised 5/31/2010 2Motion Along a Line• Position & Displacement• Speed & Velocity• Acceleration• Describing motion in 1D• Free FallMFMcGraw- PHY 1410 Ch_02b-Revised 5/31/2010 3Introduction•Kinematics - Concepts needed to describe motion - displacement, velocity & acceleration.•Dynamics - Deals with the effect of forces on motion.•Mechanics - Kinematics + DynamicsMFMcGraw- PHY 1410 Ch_02b-Revised 5/31/2010 4Goals of Chapter 2Develop an understanding of kinematics that comprehends the interrelationships among•physical intuition•equations•graphical representationsWhen we finish this chapter you should be able to move easily among these different aspects.MFMcGraw- PHY 1410 Ch_02b-Revised 5/31/2010 5Kinematic Quantities OverviewThe words speed and velocity are used interchangably in everyday conversation but they have distinct meanings in the physics world.MFMcGraw- PHY 1410 Ch_02b-Revised 5/31/2010 6The position (x) of an object describes its location relative to some origin or other reference point.Position & Displacement0x20x1The position of the red ball differs in the two shown coordinate systems.MFMcGraw- PHY 1410 Ch_02b-Revised 5/31/2010 70x (cm)2121The position of the ball iscm 2xThe + indicates the direction to the right of the origin.MFMcGraw- PHY 1410 Ch_02b-Revised 5/31/2010 80x (cm)2121The position of the ball iscm 2xrxThe  indicates the direction to the left of the origin.MFMcGraw- PHY 1410 Ch_02b-Revised 5/31/2010 9The displacement is the change in an object’s position. It depends only on the beginning and ending positions.ifxxx All Δ quantities will have the final value 1st and the inital value last.MFMcGraw- PHY 1410 Ch_02b-Revised 5/31/2010 100x (cm)2121cm 4cm 2 cm 2ifxxxExample: A ball is initially at x = +2 cm and is moved to x = -2 cm. What is the displacement of the ball?MFMcGraw- PHY 1410 Ch_02b-Revised 5/31/2010 11Example: At 3 PM a car is located 20 km south of its starting point. One hour later its is 96 km farther south. After two more hours it is 12 km south of the original starting point.(a) What is the displacement of the car between 3 PM and 6 PM?xi = –20 km and xf = –12 km  km 8km 20 km 12 ifxxxUse a coordinate system where north is positive.MFMcGraw- PHY 1410 Ch_02b-Revised 5/31/2010 12(b) What is the displacement of the car from the starting point to the location at 4 pm?(c) What is the displacement of the car from 4 PM to 6 PM?Example continuedxi = 0 km and xf = –96 km  km 96km 0 km 96 ifxxxxi = –96 km and xf = –12 km  km 84km 96 km 12 ifxxxMFMcGraw- PHY 1410 Ch_02b-Revised 5/31/2010 13Velocity is a vector that measures how fast and in what direction something moves.Speed is the magnitude of the velocity. It is a scalar.Velocity: Rate of Change of PositionMFMcGraw- PHY 1410 Ch_02b-Revised 5/31/2010 14txvx,av In 1-dimension the average velocity isvav is the constant speed and direction that results in the same displacement in a given time interval. tripof time traveleddistancespeed Average MFMcGraw- PHY 1410 Ch_02b-Revised 5/31/2010 15On a graph of position versus time, the average velocity is represented by the slope of a chord.x (m)t (sec)t1t2x1x21212,av velocityAveragettxxvxMFMcGraw- PHY 1410 Ch_02b-Revised 5/31/2010 16txvtxlim0 velocityousInstantaneThis is represented by the slope of a line tangent to the curve on the graph of an object’s position versus time.x (m)t (sec)MFMcGraw- PHY 1410 Ch_02b-Revised 5/31/2010 17The area under a velocity versus time graph (between the curve and the time axis) gives the displacement in a given interval of time.vx (m/s)t (sec)MFMcGraw- PHY 1410 Ch_02b-Revised 5/31/2010 18Example (text problem 2.11): Speedometer readings are obtained and graphed as a car comes to a stop along a straight-line path. How far does the car move between t = 0 and t = 16 seconds? Since there is not a reversal of direction, the area between the curve and the time axis will represent the distance traveled.MFMcGraw- PHY 1410 Ch_02b-Revised 5/31/2010 19Example continued:The rectangular portion has an area of Lw = (20 m/s)(4 s) = 80 m. The triangular portion has an area of ½bh = ½(8 s) (20 m/s) = 80 m. Thus, the total area is 160 m. This is the distance traveled by the car.MFMcGraw- PHY 1410 Ch_02b-Revised 5/31/2010 20The Most Important Graph- V vs TArea under the curve gives DISTANCE.The slope of the curve gives the ACCELERATION.The values of the curve gives the instantaneous VELOCITY.Negative areas are possible.MFMcGraw- PHY 1410 Ch_02b-Revised 5/31/2010 21Acceleration: Rate of Change of Velocitytvaxxav,onaccelerati Averagetvaxtxlim0onaccelerati ousInstantaneThese have interpretations similar to vav and v.MFMcGraw- PHY 1410 Ch_02b-Revised 5/31/2010 22Example (text problem 2.29): The graph shows speedometer readings as a car comes to a stop. What is the magnitude of the acceleration at t = 7.0 s? The slope of the graph at t = 7.0 sec is  21212avm/s 5.2s 412m/s 200ttvvtvaxMFMcGraw- PHY 1410 Ch_02b-Revised 5/31/2010 23Motion Along a Line With Constant Accelerationxavvtavvvtatvxxxxixfxxixfxxxixif221222For constant acceleration the kinematic equations are:2,av,avfxixxxvvvtvxAlso:MFMcGraw- PHY 1410 Ch_02b-Revised 5/31/2010 24A Modified Set of Equations2f i ix xfx ix x2 2fx ix x1x = x + vΔt + a Δt2v = v + aΔtv = v + 2aΔxFor constant acceleration the kinematic equations are:f i av,xix fxav,xx = x + vΔtv + vv =2Also:MFMcGraw- PHY 1410 Ch_02b-Revised 5/31/2010 25Visualizing Motion Along a Line with Constant AccelerationMotion diagrams for three carts:MFMcGraw- PHY 1410 Ch_02b-Revised 5/31/2010 26Graphs of x, vx, ax for each of the three cartsMFMcGraw- PHY