# Chapter 2: One-Dimensional Motion

Difficulty Level:

**At Grade**Created by: CK-12

**Credit**: Wouter Kiel

**Source**: http://www.flickr.com/photos/wouterkiel/3443427312/

**License**: CC BY-NC 3.0

One-dimensional motion means moving forwards and/or backwards along a straight line, and is the simplest form of motion to study. The core of learning this is understanding *rate*s, which is how any quantity changes over time. Key rates we will study are speed, velocity, and acceleration.

## Chapter Outline

- 2.1. Locating an Object: Distance and Displacement
- 2.2. Speed and Velocity in One Dimension
- 2.3. Average Speed, Velocity, and Instantaneous Velocity
- 2.4. Uniform Acceleration
- 2.5. The Kinematic Equations

### Chapter Summary

- Displacement is the difference between the ending position and starting position of motion. It is a vector quantity.
- Velocity is the rate of change of position. It is vector quantity.
- Average speed can be computed finding the total distance divided by the total time or by a weighted average.
- The slope of a line in the position-time plane represents velocity.
- The area in the acceleration-time plane represents a change in velocity.
- Area in the velocity-time plane represents a change in position (displacement).
- The slope of a line in the velocity-time plane represents acceleration.
- The gravitational acceleration near the surface of the earth is very close to \begin{align*}9.8 \ m/s^2\end{align*}.
- The kinematic equations of motion in one dimension are:

- @$\begin{align*}v_{avg} = \frac{\Delta x}{\Delta t}\end{align*}@$, always true
- @$\begin{align*}a_{avg} = \frac{\Delta v}{\Delta t}\end{align*}@$, always true
- @$\begin{align*}v_f = at+v_i\end{align*}@$, constant acceleration only
- @$\begin{align*}v_{avg}=\frac{(v_f+v_i)}{2}\end{align*}@$, constant acceleration only
- @$\begin{align*}x = \frac{1}{2}at^2+v_it+x_i\end{align*}@$, constant acceleration only
- @$\begin{align*}v{_f}^2 = v{_i}^2+2a \Delta x\end{align*}@$, constant acceleration only

### Image Attributions

**[1]****^**Credit: Wouter Kiel; Source: http://www.flickr.com/photos/wouterkiel/3443427312/; License: CC BY-NC 3.0

## Description

Covers the kinematics of linear motion, including position, speed, velocity, and acceleration along with how to solve kinematic equations.

## Difficulty Level:

At Grade## Authors:

## Editors:

## Subjects:

## Date Created:

Dec 05, 2014## Last Modified:

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