College Physics For AP® Courses

1 2 KINEMATICSF igure motion of an American kestrel through the air can be described by the bird's displacement, speed, velocity, and acceleration. When itflies in a straight line without any change in direction, its motion is said to be one dimensional. (credit: Vince Maidens, Wikimedia Commons) chapter Vectors, Scalars, and Coordinate Time, Velocity, and Motion Equations for Constant Acceleration in One Problem-Solving Basics for One Dimensional Falling Graphical Analysis of One Dimensional MotionConnection for AP CoursesObjects are in motion everywhere we look. Everything from a tennis game to a space-probe flyby of the planet Neptune involvesmotion. When you are resting, your heart moves blood through your veins. Even in inanimate objects, there is a continuousmotion in the vibrations of atoms and molecules. Questions about motion are interesting in and of themselves:How long will ittake for a space probe to get to Mars?

2 Where will a football land if it is thrown at a certain angle?Understanding motion will not only provide answers to these questions, but will be key to understanding more advancedconcepts in Physics . For example, the discussion of force in chapter 4 will not fully make sense until you understandacceleration. This relationship between force and acceleration is also critical to understanding Big Idea , this unit will explore the topic of reference frames, a critical component to quantifying how things move. If you haveever waved to a departing friend at a train station, you are likely familiar with this idea. While you see your friend move awayfrom you at a considerable rate, those sitting with her will likely see her as not moving. The effect that the chosen referenceframe has on your observations is substantial, and an understanding of this is needed to grasp both Enduring Understanding Essential Knowledge formal study of Physics begins withkinematics,which is defined as thestudy of motion without considering its causes.

3 Inone- and two-dimensional kinematics we will study only themotionof a football, for example, without worrying about what forcescause or change its motion. In this chapter , we examine the simplest type of motion namely, motion along a straight line, orone-dimensional motion. Later, in two-dimensional kinematics, we apply concepts developed here to study motion along curvedpaths (two- and three-dimensional motion), for example, that of a car rounding a content in this chapter supports:Big Idea 3 The interactions of an object with other objects can be described by 2 | Kinematics33 Enduring Understanding All forces share certain common characteristics when considered by observers in inertial Knowledge An observer in a particular reference frame can describe the motion of an object using suchquantities as position, displacement, distance, velocity, speed, and DisplacementFigure cyclists in Vietnam can be described by their position relative to buildings and a canal.

4 Their motion can be described by their changein position, or displacement, in the frame of reference. (credit: Suzan Black, Fotopedia)Learning ObjectivesBy the end of this section, you will be able to: Define position, displacement, distance, and distance traveled in a particular frame of reference. Explain the relationship between position and displacement. Distinguish between displacement and distance traveled. Calculate displacement and distance given initial position, final position, and the path between the information presented in this section supports the following AP learning objectives and science practices: student is able to express the motion of an object using narrative, mathematical, and graphicalrepresentations.( , , ) student is able to analyze experimental data describing the motion of an object and is able to express theresults of the analysis using narrative, mathematical, and graphical representations.

5 ( )PositionIn order to describe the motion of an object, you must first be able to describe itsposition where it is at any particular precisely, you need to specify its position relative to a convenient reference frame. Earth is often used as a referenceframe, and we often describe the position of an object as it relates to stationary objects in that reference frame. For example, arocket launch would be described in terms of the position of the rocket with respect to the Earth as a whole, while a professor'sposition could be described in terms of where she is in relation to the nearby white board. (SeeFigure ) In other cases, weuse reference frames that are not stationary but are in motion relative to the Earth. To describe the position of a person in anairplane, for example, we use the airplane, not the Earth, as the reference frame. (SeeFigure )DisplacementIf an object moves relative to a reference frame (for example, if a professor moves to the right relative to a white board or apassenger moves toward the rear of an airplane), then the object's position changes.

6 This change in position is known asdisplacement. The word displacement implies that an object has moved, or has been is thechange in positionof an object:( ) x=xf x0,where xis displacement,xfis the final position, andx0is the initial 2 | KinematicsThis content is available for free at this text the upper case Greek letter (delta) always means change in whatever quantity follows it; thus, xmeanschange in position. Always solve for displacement by subtracting initial positionx0from final that the SI unit for displacement is the meter (m) (seePhysical Quantities and Units), but sometimes kilometers, miles,feet, and other units of length are used. Keep in mind that when units other than the meter are used in a problem, you may needto convert them into meters to complete the professor paces left and right while lecturing. Her position relative to the blackboard is given byx. The+2 .0 mdisplacement of theprofessor relative to the blackboard is represented by an arrow pointing to the passenger moves from his seat to the back of the plane.

7 His location relative to the airplane is given byx. The 4 m displacement of thepassenger relative to the plane is represented by an arrow toward the rear of the plane. Notice that the arrow representing his displacement is twice aslong as the arrow representing the displacement of the professor (he moves twice as far) inFigure that displacement has a direction as well as a magnitude. The professor's displacement is m to the right, and the airlinepassenger's displacement is m toward the rear. In one-dimensional motion, direction can be specified with a plus or minussign. When you begin a problem, you should select which direction is positive (usually that will be to the right or up, but you arefree to select positive as being any direction). The professor's initial position isx0= mand her final position isxf= 3 .5 m. Thus her displacement is( ) x=xf x0= 3 .5 m m = + this coordinate system, motion to the right is positive, whereas motion to the left is negative.

8 Similarly, the airplane passenger'sinitial position isx0= 6 .0 mand his final position isxf= 2 .0 m, so his displacement isChapter 2 | Kinematics35( ) x=xf x0= 2. 0 m m = displacement is negative because his motion is toward the rear of the plane, or in the negativexdirection in our displacement is described in terms of direction, distance is defined to bethe magnitude or size ofdisplacement between two positions. Note that the distance between two positions is not the same as the distance traveledbetween traveledisthe total length of the path traveled between two positions. Distance has no direction and,thus, no sign. For example, the distance the professor walks is m. The distance the airplane passenger walks is Alert: Distance Traveled vs. Magnitude of DisplacementIt is important to note that thedistance traveled, however, can be greater than the magnitude of the displacement (bymagnitude, we mean just the size of the displacement without regard to its direction; that is, just a number with a unit).

9 Forexample, the professor could pace back and forth many times, perhaps walking a distance of 150 m during a lecture, yet stillend up only m to the right of her starting point. In this case her displacement would be + m, the magnitude of herdisplacement would be m, but the distance she traveled would be 150 m. In kinematics we nearly always deal withdisplacement and magnitude of displacement, and almost never with distance traveled. One way to think about this is toassume you marked the start of the motion and the end of the motion. The displacement is simply the difference in theposition of the two marks and is independent of the path taken in traveling between the two marks. The distance traveled,however, is the total length of the path taken between the two Your UnderstandingA cyclist rides 3 km west and then turns around and rides 2 km east. (a) What is her displacement? (b) What distance doesshe ride? (c) What is the magnitude of her displacement?

10 SolutionFigure (a) The rider's displacement is x=xf x0= 1 km. (The displacement is negative because we take east to bepositive and west to be negative.)(b) The distance traveled is3 km + 2 km = 5 km.(c) The magnitude of the displacement is1 2 | KinematicsThis content is available for free at Vectors, Scalars, and Coordinate SystemsFigure motion of this Eclipse Concept jet can be described in terms of the distance it has traveled (a scalar quantity) or its displacement in aspecific direction (a vector quantity). In order to specify the direction of motion, its displacement must be described based on a coordinate system. Inthis case, it may be convenient to choose motion toward the left as positive motion (it is the forward direction for the plane), although in many cases,thex-coordinate runs from left to right, with motion to the right as positive and motion to the left as negative. (credit: Armchair Aviator, Flickr)Learning ObjectivesBy the end of this section, you will be able to: Define and distinguish between scalar and vector quantities.