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# Chapter 2: One-Dimensional Motion

Difficulty Level: At Grade Created by: CK-12

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 rates, which is how any quantity changes over time. Key rates we will study are speed, velocity, and acceleration.

Chapter Outline

### 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 9.8 m/s2\begin{align*}9.8 \ m/s^2\end{align*}.
• The kinematic equations of motion in one dimension are:
1. vavg=ΔxΔt\begin{align*}v_{avg} = \frac{\Delta x}{\Delta t}\end{align*}, always true
2. aavg=ΔvΔt\begin{align*}a_{avg} = \frac{\Delta v}{\Delta t}\end{align*}, always true
3. vf=at+vi\begin{align*}v_f = at+v_i\end{align*}, constant acceleration only
4. vavg=(vf+vi)2\begin{align*}v_{avg}=\frac{(v_f+v_i)}{2}\end{align*}, constant acceleration only
5. x=12at2+vit+xi\begin{align*}x = \frac{1}{2}at^2+v_it+x_i\end{align*}, constant acceleration only
6. vf2=vi2+2aΔx\begin{align*}v{_f}^2 = v{_i}^2+2a \Delta x\end{align*}, constant acceleration only

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Date Created:
Nov 05, 2015