Index for
Chapter 3
Linear Motion
1. Motion Diagrams
- motion diagram
2. Displacement Vectors
- displacement vectors
- Displacement (\(\Delta x\)) measured in m
3. Average Velocity
- time interval
- \(\vec v_{avg}={\Delta\vec x\over\Delta t}\)
5. Acceleration
- acceleration
- acceleration due to gravity
- Acceleration (\(\vec a\)) measured in m/s2
- \(g=9.8\u{N/kg}=9.8\u{m/s^2}\)
6. Change in Velocity
- \(\Delta A=A_f-A_i\)
- \(A_f=A_i+\Delta A\)
7. Vector Acceleration
- \(\vec a_{avg}={\Delta\vec v\over\Delta t}\)
8. Frames of Reference
- frame of reference
- inertial
9. Uniform Circular Motion
- centrifugal pseudoforce
- \(\displaystyle{a_c={v^2\over r}}\) for an object in uniform circular motion
10. Free Fall
- free fall
11. Weightlessness
- weightlessness
13. Graphing Position
- turning point
14. Slopes
- The slope of a position graph gives you the velocity.
15. Graphing Velocity
- turning point
- the slope of the velocity graph is the acceleration.
16. Constant Acceleration
- \(v_f=v_i+a\Delta t\)
- \(\Delta x=\frac12(v_i+v_f)\Delta t\)
- In a one-dimensional constant-acceleration problem,
we must be given three of the five variables
in order to solve for the rest.
17. The Five Equations
- don't-know-don't-care
- $$\begin{align}
v_f&=v_i+a\Delta t &\color{blue}{\hbox{no}\,\Delta x}\\
\Delta x&=\frac{1}{2}(v_i+v_f)\Delta t &\color{blue}{\hbox{no}\,a}\\
\Delta x&=v_i\Delta t+\frac12a\Delta t^2 &\color{blue}{\hbox{no}\,v_f}\\
\Delta x&=v_f\Delta t-\frac12a\Delta t^2 &\color{blue}{\hbox{no}\,v_i}\\
v_f^2&=v_i^2+2a\Delta x &\color{blue}{\hbox{no}\,\Delta t}\\
\end{align}$$