Chapter 2:Motion along a straight lineDescribing Motion …Average speed and velocityAverage velocityInstantaneous velocityAverage Velocity (example)Instantaneous VelocityAccelerationAverage accelerationKinematics in one dimension (cont.)RecapExamplesConceptual ExampleExample of graphic solution: Catching a speeder (Example 2.9)Ex2-3: Engine traveling on railSlide 16Kinematics equations for constant accelerationAll objects fall with the same constant acceleration!!Testing Kinetics for a=9.80m/s2Slide 20Slide 21Problem: Vertical motionSlide 23Slide 24Slide 251-D motions in the gravitational fieldChapter 2:Motion along a straight lineTranslational Motion and Rotational MotionToday LaterDescribing Motion …Coordinates  Position (displacement)  Velocity  Acceleration a) Motion with zero acceleration b) Motion with non-zero accelerationAverage speed and velocity )_()_(_timetotaltntdisplacemetotalxvelocityaver agev dtdxti metntdisplacemexve l ocityvt)()(lim0•Instantaneous velocity, velocity at a given instantSpeedSpeed is just the magnitude of is just the magnitude of velocityvelocity!! The “how fast” without accounting for the The “how fast” without accounting for the direction.direction.•Average velocity = total displacement covered Average velocity = total displacement covered per total elapsed time,per total elapsed time,•Average speed = total distance covered per total elapsed time,Average speed = total distance covered per total elapsed time,Average velocityΔtΔxv Instantaneous velocity0 ΔtwhenΔtΔxv limAverage Velocity (example)x (meters)t (seconds)26-24What is the average velocity over the first 4 seconds ?A) -2 m/s D) not enough information to decide.C) 1 m/sB) 4 m/s1 2 430x (meters)t (seconds)26-24What is the instantaneous velocity at the fourth second ?A) 4 m/s D) not enough information to decide.C) 1 m/sB) 0 m/s1 2 43Instantaneous VelocityAcceleration•We say that things which have changing velocity are “ac celerating”•Acceleration is the “Rate of change of velocity”•You hit the a ccelerator in your car to speed up–(Ok…It’s true you also hit it to stay at constant velocity, but that’s because friction is slowing you down…we’ll get to that later…)Average accelerationΔtΔva Unit of acceleration:(m/s)/s=m/s2Meters per second squaredKinematics in one dimension (cont.)Motion with constant acceleration.From the formula for average accelerationtvva0atvv 0atvatvvvvv21))((21)(210000txvvelocityAverage 200021)21( attvtatvtvxx We findOn the other handThen we can findRecap•So for constant acceleration we find:atvv0200at21tvxx a constxavtttExamples•Can a car have uniform speed and non-constant velocity?•Can an object have a positive average velocity over the last hour, and a negative instantaneous velocity?Conceptual Example•If the velocity of an object is zero, does it mean that the acceleration is zero?–Example?•If the acceleration is zero, does that mean that the velocity is zero?–Example?Example of graphic solution: Catching a speeder (Example 2.9)Ex2-3: Engine traveling on railKinematics equations for constant acceleration atvv 020021attvxx )(20202xxavv tvvxx )2(00All objects fall with the same constant acceleration!!Testing Kinetics for a=9.80m/s2Problem: Vertical motionStone is thrown vertically upward1-D motions in the gravitational