Ch. 2: Describing Motion: Kinematics in One DimensionTerminologyA Brief Overview of the CourseSlide 4Sect. 2-1: Reference Frames & DisplacementCoordinate AxesSlide 7Displacement & DistanceDisplacementSlide 10Vectors and ScalarsSlide 12Sect. 2-2: Average VelocityAverage Velocity, Average SpeedSlide 15Example 2-1Slide 17Slide 18Slide 19Slide 20Slide 21Sect. 2-4: AccelerationExample 2-4: Average AccelerationSlide 24Conceptual QuestionSlide 26Example 2-6: Car Slowing DownSlide 28DecelerationSlide 30Slide 31Slide 32Slide 33One-Dimensional Kinematics ExamplesSlide 35Slide 36Slide 37Slide 38Slide 39Slide 40Slide 41Slide 42Slide 43Ch. 2: Describing Motion: Kinematics in One DimensionTerminology •Classical Mechanics = The study of objects in motion. –2 parts to mechanics.•Kinematics = A description of HOW objects move. –Chapters 2 & 4 (Ch. 3 is mostly math!)•Dynamics = WHY objects move.–Introduction of the concept of FORCE.–Causes of motion, Newton’s Laws–Most of the course after Chapter 4For a while, assume ideal point masses (no physical size). Later, extended objects with size.A Brief Overview of the Course “Point” Particles & Large Masses•Translational Motion = Straight line motion. –Chapters 2,3,4,5,6,7,8,9•Rotational Motion = Moving (rotating) in a circle.–Chapters 5,6,10,11•Oscillations = Moving (vibrating) back & forth in same path.–Chapter 1 Continuous Media•Waves, Sound–Chapters 15,16 •Fluids = Liquids & Gases–Chapter 13 Conservation Laws: Energy, Momentum, Angular Momentum–Just Newton’s Laws expressed in other forms! THE COURSE THEME IS NEWTON’S LAWS OF MOTION!!Chapter 2 Topics•Reference Frames & Displacement•Average Velocity•Instantaneous Velocity•Acceleration•Motion at Constant Acceleration•Solving Problems•Freely Falling ObjectsSect. 2-1: Reference Frames & Displacement •Every measurement must be made with respect to a reference frame. Usually, the speed is relative to the Earth.•For example, if you are sitting on a train & someone walks down the aisle, the person’s speed with respect to the train is a few km/hr, at most. The person’s speed with respect to the ground is much higher. •Specifically, if a person walks towards the front of a train at 5 km/h (with respect to the train floor) & the train is moving 80 km/h with respect to the ground. The person’s speed, relative to the ground is 85 km/h.Coordinate Axes •Usually, we define a reference frame using a standard coordinate axes. (But the choice of reference frame is arbitrary & up to us, as we’ll see later!)•2 Dimensions (x,y)•Note, if its convenient, we could reverse + & - !+,+- ,+- , -+ , -A standard set of xy (Cartesian or rectangular) coordinate axesCoordinate Axes •In 3 Dimensions (x,y,z)•We define directions using these.First OctantDisplacement & Distance Distance traveled by an object  Displacement of the object!•Displacement  The change in position of an object.•Displacement is a vector (magnitude & direction). •Distance is a scalar (magnitude).In this figure,The Distance = 100 m. The Displacement = 40 m East.Displacementx1 = 10 m, x2 = 30 mDisplacement  ∆x = x2 - x1 = 20 m∆  Greek letter “delta” meaning “change in”The arrow represents the displacement (in meters).t1t2 timesx1 = 30 m, x2 = 10 mDisplacement  ∆x = x2 - x1 = - 20 mDisplacement is a VECTORVectors and Scalars •Many quantities in physics, like displacement, have a magnitude and a direction. Such quantities are called VECTORS.–Other quantities which are vectors: velocity, acceleration, force, momentum, ...•Many quantities in physics, like distance, have a magnitude only. Such quantities are called SCALARS.–Other quantities which are scalars: speed, temperature, mass, volume, ...•The Text uses BOLD letters to denote vectors. •I usually denote vectors with arrows over the symbol.•In one dimension, we can drop the arrow and remember that a + sign means the vector points to right & a minus sign means the vector points to left.Sect. 2-2: Average Velocity Average Speed  (Distance traveled)/(Time taken)Average Velocity  (Displacement)/(Time taken)•Velocity: Both magnitude & direction describing how fast an object is moving. A VECTOR. (Similar to displacement).•Speed: Magnitude only describing how fast an object is moving. A SCALAR. (Similar to distance).•Units: distance/time = m/sScalar→Vector→Average Velocity, Average Speed •Displacement from before. Walk for 70 s.•Average Speed = (100 m)/(70 s) = 1.4 m/s•Average velocity = (40 m)/(70 s) = 0.57 m/s•In general:∆x = x2 - x1 = displacement∆t = t2 - t1 = elapsed timeAverage Velocity: = (x2 - x1)/(t2 - t1)  timest2t1Bar denotes averageExample 2-1 •Person runs from x1 = 50.0 m to x2 = 30.5 m in ∆t = 3.0 s. ∆x = -19.5 mAverage velocity = (∆x)/(∆t) = -(19.5 m)/(3.0 s) = -6.5 m/s. Negative sign indicates DIRECTION, (negative x direction)Sect. 2-3: Instantaneous Velocity  velocity at any instant of time  average velocity over an infinitesimally short time•Mathematically, instantaneous velocity: ratio considered as a whole for smaller & smaller ∆t. As you should know, mathematicians call this a derivative. Instantaneous velocity v ≡ time derivative of displacement xThese graphs show (a) constant velocity  and (b) varying velocity instantaneous velocity = average velocityinstantaneous velocity  average velocityThe instantaneous velocity is the average velocity in the limit as the time interval becomes infinitesimally short.Ideally, a speedometer would measure instantaneous velocity; in fact, it measures average velocity, but over a very short time interval.On a graph of a particle’s position vs. time, the instantaneous velocity is the slope of the tangent to the curve at any point.A jet engine moves along a experimental track (called the x axis) as shown. Treat the engine as if it were a particle. Its position as a function of time is given by the equation x = At2 + B, where A = 2.10 m/s2 & B = 2.80 m. (a) Find the displacement of the engine during the time interval from t1 = 3.00 s to t2 = 5.00 s. (b) Find the average velocity during this time interval. (c) Determine the magnitude of the instantaneous velocity at t = 5.0 s.Example 2-3: Given x as a function of t.Work on the board!Sect. 2-4: Acceleration