# Motion in a Straight Line

Updated: Sep 25, 2021

By Sumay and Aila McPhail

In this article we will be summarizing the crash course physics playlist. Physics is the study of how the world and the universe works. Today, what we will be talking about in particular is motion in a straight line. Motion in a straight line is also called one-dimensional motion meaning you can only go right to left. The three topics we will cover are...time, position, velocity, and acceleration, delta and the definition of acceleration, and the displacement curve. These are all relating to motion in a straight line and how you can use this to calculate your exact position in the universe.

Time, position, velocity and acceleration are all factors that define your place in the universe: Time (the amount of time, how long), Position (where you are and where you were), Velocity (how your position changes over time) and Acceleration (how your velocity is changing). To think about all these factors at once you’ll have to link them together using something called the kinematic equations which we will be talking about in the next two paragraphs. The way you would refer to your position on a one-dimensional scale is that your first position is zero and when you move you can either add or subtract from the initial number. To find the average velocity in a certain time you would take the change in position and divide it by the change in time. To find the average acceleration you would divide the change in velocity over the change in time.

The symbol for the change in some quantity is called delta and looks like this: Δ. So if you were calculating the average velocity and position is x and time is t, you would say Δx / Δt meaning that you are dividing the change in position over the change in time. You can also use Δ to equate the average acceleration. Let’s say velocity is v and time is t then the average acceleration would be Δv / Δt. The first kinematic equation is called the definition of acceleration and is v = v0 + *a*t. v = average velocity, *v0 = the velocity at time 0 (initial velocity), a = acceleration, and t = time. This equation is just another way of calculating the average acceleration. And basically is just rearranging the variables in the equation we mentioned earlier that calculates the average acceleration like this: average acceleration = Δv / Δt … v = velocity and t = time.

The first kinematic equation only links velocity, acceleration, and time. The next kinematic equation called the displacement curve also links in position. So what is displacement? Displacement is the shortest distance from your starting point and ending point. If you were to move in a zigzag line from point a to point b, your displacement would be the shortest distance from point a to point b. The displacement curve kinematic equation calculates your displacement. The simplest way to calculate your displacement is by taking your current position and subtracting your initial position (your position at time 0). The displacement curve kinematic equation takes your velocity, time, and acceleration to calculate your displacement. The actual kinematic equation displacement curve is v0 * t + (½) * a * t^2 , where v0 = Initial velocity (velocity at time 0), t = time, and a = acceleration.

Here is an example of using the displacement curve equation! So the variables that we need are time, acceleration and the initial velocity. Let's just give these variable's some value just so you can see the equation being calculated.

**v0 (initial velocity)** = 0

**t (time)** = 10

**a (acceleration)** = 3

So then we would input these values into the equation and what we would be trying to solve is this: 0 * 10 + (1/2) * 3 * 10^2

Here is how we would go about trying to solve this:

**0 * 10 + (1/2) * 3 * 10^2**

= 0 * 10 + (1/2) * 3 * 100

= 0 + (1/2) * 3 * 100

= 0 + 1.5 * 100

= 0 + 150

= 150

Now we know that the displacement is 150 only given the values for time, initial velocity and the acceleration! As you can see this is very useful whenever you need to calculate displacement but may not have the resources to know the value for what the position was and only have limited knowledge. These equations may seem complicated and unnecessary but all they are is ways that we can understand the world better by using these numbers to represent things in the real world like displacement!

In this article we talked about time, position, velocity, and acceleration, delta and the definition of acceleration, and the displacement curve. You can use the kinematic equations to calculate things like how fast things are going. Learning about time, position, velocity, and acceleration can show you your exact place in the universe, and how it’s moving. Physics is a great way to learn about everything since everything has to operate within the laws of physics. If you would like to learn more we would definitely recommend watching the crash course physics playlist on YouTube.