7.1: Prelude to One-Dimensional Kinematics Our formal study of physics begins with kinematics which is defined as the study of motion without considering its causes. In one-dimensional kinematics and Two-Dimensional Kinematics we will study only the motion of a football, for example, without worrying about what forces cause or change its motion. Such considerations come in other chapters. In this chapter, we examine the simplest type of motion—namely, motion along a straight line, or one-dimensional motion. 7.2: Displacement Kinematics is the study of motion without considering its causes. In this chapter, it is limited to motion along a straight line, called one-dimensional motion. Displacement is the change in position of an object. 7.3: Vectors, Scalars, and Coordinate Systems A vector is any quantity that has magnitude and direction. A scalar is any quantity that has magnitude but no direction. Displacement and velocity are vectors, whereas distance and speed are scalars. In one-dimensional motion, direction is specified by a plus or minus sign to signify left or right, up or down, and the like. 7.4: Time, Velocity, and Speed There is more to motion than distance and displacement. Questions such as, “How long does a foot race take?” and “What was the runner’s speed?” cannot be answered without an understanding of other concepts. In this section we add definitions of time, velocity, and speed to expand our description of motion. 7.5: Acceleration Acceleration is the rate at which velocity changes. In symbols, average acceleration a− is a−= ΔvΔt=vf−v0tf−t0. The SI unit for acceleration is m/s2 . Acceleration is a vector, and thus has a both a magnitude and direction. Acceleration can be caused by either a change in the magnitude or the direction of the velocity. Instantaneous acceleration a is the acceleration at a specific instant in time. Deceleration is an acceleration with a direction opposite to that of the velocity. 7.6: Kinematics in Two Dimensions - An Introduction An old adage states that the shortest distance between two points is a straight line. The two legs of the trip and the straight-line path form a right triangle. 7.7: Projectile Motion Projectile motion is the motion of an object thrown or projected into the air, subject to only the acceleration of gravity. The object is called a projectile, and its path is called its trajectory. The motion of falling objects is a simple one-dimensional type of projectile motion in which there is no horizontal movement. In this section, we consider two-dimensional projectile motion, such as that of a football or other object for which air resistance is negligible. 7.8: Development of Force Concept 7.9: Newton’s First Law of Motion- Inertia Experience suggests that an object at rest will remain at rest if left alone, and that an object in motion tends to slow down and stop unless some effort is made to keep it moving. 7.10: Newton’s Second Law of Motion- Concept of a System 7.11: Newton’s Third Law of Motion- Symmetry in Forces There is a passage in the musical Man of la Mancha that relates to Newton’s third law of motion. Sancho, in describing a fight with his wife to Don Quixote, says, “Of course I hit her back, Your Grace, but she’s a lot harder than me and you know what they say, ‘Whether the stone hits the pitcher or the pitcher hits the stone, it’s going to be bad for the pitcher.’” This is exactly what happens whenever one body exerts a force on another—the first also experiences a force (equal in magnitude and 7.12: Linear Momentum and Force The scientific definition of linear momentum is consistent with most people’s intuitive understanding of momentum: a large, fast-moving object has greater momentum than a smaller, slower object. Linear momentum is defined as the product of a system’s mass multiplied by its velocity. Momentum is directly proportional to the object’s mass and also its velocity. Thus the greater an object’s mass or the greater its velocity, the greater its momentum. 7.13: Impulse The effect of a force on an object depends on how long it acts, as well as how great the force is. A very large force acting for a short time had a great effect on the momentum of the tennis ball. A small force could cause the same change in momentum, but it would have to act for a much longer time.