- The 1-D kinematic equations of motion:
\begin{itemize}
- $v=\Delta x/\Delta t$
- $a= \Delta v/\Delta t$
- $d=v_0t+\frac12 at^2$
- $v_f^2-v_0^2=2ad$
Remark
Note that these are for constant acceleration. Also, as mentioned in class, the change in acceleration over time is called jerk. So, the equatiosn above only apply for zero jerk.
Idea: 2-D
We'll work with 2-D more extensively next week, but here are a couple notes to help you out for the couple two dimensional problems.
- When working in two dimensions, everything is the same, but the vectors now have "spatial direction" rather than just positive or negative. You can break down velocities into $x$ and $y$ components, but everything works the same. We still have $$\vec x = \vec v t,$$ and this is also equivalent to breaking it down into components $x = v_x t, y = v_yt$. The same goes for acceleration.
- Drawing arrows as visuals for vectors is always quite helpful as well. See this reference for how to add and subtract vectors. Being able to add and subtract vectors will be quite useful for switching reference frames.
\item Graphs can be used to analyze the relationship between $x$, $v$, and $a$: $v$ is the slope on a graph of $x$ vs $t$, for example, while $x$ is the area under the curve of a graph of $v$ vs $t$.
Tip
Reference frames of constant speed and acceleration may be used to simplify calculations.
\end{itemize}