Hello, and welcome back to MPC! Last week, we spoke about the history, significance, and counterintuitive nature of modern physics. Today, we will be preparing for our entrance into the realm of modern physics with some basic physics terminology and formulas. This post will include some math, but don’t worry — as long as you can perform division, you will be fine.

The first quantity we are going to talk about is *position*. This one is simple, for it is just what you think it is: your location. For example, let’s just say you are in New York City. That’s your position! You are *in* New York City.

Now, it does get a little more complex. Physicists like to deal with numbers. Why? Physics is considered to be a precise science, and must therefore be objective. If you were to say your position was New York City, this could have many different meanings to different people. For example, I may think that you are in Times Square. Someone else, though, may think that you are right outside of the Empire State Building. A third person may think that you are in Central Park. There is too much ambiguity! But what happens if you were to say that you were 2 feet in front of the Empire State Building’s main entrance in New York City. Now, your position is much more precise because there is very little room for debate (someone else cannot think that you are in Times Square because Times Square is not 2 feet in front of the Empire State Building’s main entrance).

Many times, position is represented by an *x* (so, I could say that you are at position *x*, if I have declared that *x* is 2 feet in front of the Empire State Building’s main entrance).

Next, we are going to talk about *displacement*. Displacement is very closely related to position. Specifically, displacement is the **change** in position. To understand this, let’s hit the road!

You are in your car, on a vacant highway, and decide to drive up to mile marker 1. Your *position *at this moment is mile marker 1 (in a given city/state). Soon, you drive to mile marker 2. Your *position* now is mile marker 2 (in a given city/state). What was your displacement? Well, you started at mile marker 1 and you are now at mile marker 2, so you have moved one 1 mile marker (2 – 1 = 1). In other words, your change in position, or displacement, is 1 mile marker. Simple! If you are you starting to think of displacement as being the same as the distance you have traveled, that’s good — it means that you are catching on (it should be noted that displacement and distance are not exactly the same, but for our purposes at the moment, we can consider them to be the same). If you consider displacement to be the same as distance, it may seem more fitting for you to say that your displacement is 1 mile (you have traveled 1 mile to reach mile marker 2), and this is indeed a more scientific way of putting it.

Quick quiz! You now move from mile marker 2 to mile marker 4. What is your displacement in doing this? If you answered 2 mile markers or 2 miles, you are correct! Note that while your displacement from mile marker 2 is 2 miles, your displacement from your original starting position (mile marker 1) is 3 miles (4 – 1 = 3).

Displacement is typically represented by *Δx*. That *Δ* is a very important symbol in math and physics. It is called a delta and means “change in.” So, *Δx* means “change in *x*.” Remember that *x* is position, so *Δx*’s fully meaning is “change in position” (just as we defined it before). Whenever you see a *Δ*, think subtraction — you are taking your starting value and subtracting it from your final value: *Δx* = final *x* – starting *x* = final position – starting position. When applied to the previous examples, it should be clear that this relationship is true (I have been including the subtraction in parentheses for each of the examples).

Up next, *velocity*. Velocity is how far you are moving every second: it is your displacement per unit of time. Going back to the previous example, let’s just say you move from mile marker 1 to mile marker 2 in 1 hour (you are moving very slowly). Well, we already said that your displacement in this scenario is 1 mile. If we let our unit of time be 1 hour, then your velocity is 1 mile per 1 hour, or 1 mile per hour. What if we make our unit of time 1 minute? Well, 1 hour is the same as 60 minutes, so you are moving at 1 mile for every 60 minutes, or 1 mile per 60 minutes. This can be represented as (1 mile) / (60 minutes). If you were to carry out the division, you would get your velocity to be 0.0166… miles per minute. Just as displacement is very similar to distance, velocity is very similar to speed.

Who cares about velocity? It is actually quite powerful! In the previous example, we said that you were moving at 1 mile per hour. What this really means is that in one hour, you are traveling 1 mile. Let’s just say we wanted to know how far you would travel if you were traveling for 2 hours? Assuming you are moving at the same 1 mile per hour velocity throughout your journey, you will be able to travel 2 miles (twice as far): in the first hour you will travel 1 mile and in the second hour you will travel another mile, giving us 2 miles in total. What if we want to know how long you have been traveling for if you have only gone ½ or 0.5 miles? Once again assuming that you have been going at 1 mile per hour the whole time, you have only been traveling for ½ hours (30 minutes) to go ½ miles. If this is confusing, try spending a few moments thinking about it: If you can go a full 1 mile for each hour that you travel, and you only need to go half of that 1 mile distance, you would only have to travel for half as long. The equation for velocity is *v* = *Δx* / *t*.

And with that, we are ready to jump into our first branch of modern physics: relativity. Get ready, because this is going to be exciting!

(featured image: https://cpms.byu.edu/wp-content/uploads/2015/09/equations.jpg)