Basic Math and Physics

[latexpage]
It has always been my aim to provide as much of a log about creating a racing simulation as I can, including the mathematics of the simulation and other details. I’ve just setup something on the blog to allow. So here we will start be some of the extremely basic math/physics that an average high-schooler would understand.

\begin{equation} \label{eq:sys}
\vec{F} = m\vec{A}
\end{equation}

The mass, $m$, of an object is measured in kilograms, for the SI/metric system (or Slugs for imperial system). The acceleration, $\vec{A}$, is measured in meters per second, per second; $m/s/s$ also known as $m/s^2$

Say for a moment we are confused what units $\vec{F}$ would be, how would we figure that out? Knowing the units of $m$ in $kg$ and $\vec{A}$ in $m/s^2$ then we can perform dimensional analysis and multiply the units to get:

\begin{equation}
m(kg) * \vec{A}(m/s^2) = kg*m/s^2
\end{equation}

I’ve been using this a lot recently, I’ve found it is a great way to double/triple check that the math lines up and makes sense. Another lesson I’ve learned recently is that having confidence and attacking something is a grand way to improve. Years have passed since my last official math course and my attitude / thought process remained the same, until last week. From that point on I look at math as a challenge that I’m getting better at. The viewpoint of “I suck at __” will enforce negativity, so if you are attempting to get better, stop focusing on how bad you may be at the moment and instead focus on improving.

You probably won’t go from drawing like a 5 year-old today to a Leonardo / Michelangelo tomorrow; but stay positive, take your time and put in the effort; improvements will come.