# 2: One-Dimensional Kinematics

- Page ID
- 26480

\( \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \) \( \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}} \)\(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\) \(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\)\(\newcommand{\AA}{\unicode[.8,0]{x212B}}\)

- 2.1: 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.

- 2.2: 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.

- 2.3: 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.

- 2.4: 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.

- 2.5: 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.

- 2.6: Motion Equations for Constant Acceleration in One Dimension
- We might know that the greater the acceleration of, say, a car moving away from a stop sign, the greater the displacement in a given time. But we have not developed a specific equation that relates acceleration and displacement. In this section, we develop some convenient equations for kinematic relationships, starting from the definitions of displacement, velocity, and acceleration already covered.

- 2.7: Problem-Solving Basics for One-Dimensional Kinematics
- The ability to apply broad physical principles, usually represented by equations, to specific situations is a very powerful form of knowledge. It is much more powerful than memorizing a list of facts. Analytical skills and problem-solving abilities can be applied to new situations, whereas a list of facts cannot be made long enough to contain every possible circumstance. Such analytical skills are useful both for solving problems in this text and for applying physics.

- 2.8: Falling Objects
- An object in free-fall experiences constant acceleration if air resistance is negligible. On Earth, all free-falling objects have an acceleration due to gravity g, which averages g=9.80 m/s2. Whether the acceleration a should be taken as +g or −g is determined by your choice of coordinate system. Since acceleration is constant, the kinematic equations above can be applied with the appropriate +g or −g substituted for a. For objects in free-fall, up is normally taken as positive.

- 2.9: Graphical Analysis of One-Dimensional Motion
- Graphs of motion can be used to analyze motion. Graphical solutions yield identical solutions to mathematical methods for deriving motion equations. The slope of a graph of displacement x vs. time t is velocity v. The slope of a graph of velocity v vs. time t graph is acceleration a. Average velocity, instantaneous velocity, and acceleration can all be obtained by analyzing graphs.