Hello and welcome to another episode in the Godot basics tutorial series. In this episode we will be taking a look at velocity and acceleration. There is quite a lot you can do with physics in game programming besides the usual such as speed acceleration gravity. Sometimes we need formulas to do more complex things such as calculating our initial velocity when we want to reach a certain height in our jumping function. However we're not going to go into a lot of detail in this episode. I I will go into more detail towards the end of this series however I just want to reintroduce the idea of physics and its importance in game programming. Let's start with distance. Distance is a new numerical measurement of how far apart objects or points are. Let's go over an example of distance and how we would calculate that. So let's pretend we have Dora, Who's going to school and the schools a thousand meters. So when she reaches school she would have traveled a distance of 1000 meters. Now let's pretend that she forgot her books at home.

And so she must travel an extra 1000 meters with distance we would say that Dora has traveled a total distance of 2000 meters. And one thing to keep in mind is notice how there are no arrows no arrow heads on these lines. So distance is not concerned with direction. Now another word I'd like to reintroduce to you is displacement and displacement is a vector whose length is the shortest distance from the initial to the final position of a point P undergoing motion. The big take away from displacement is that it's a vector and let's go over an example of displacement. So we have Dora in the same situation she's travelling to school and so we say that Dora has traveled a total displacement of 1000 meters And the same thing happened again. Dora has forgotten her books. And notice. How. Initially. We had her travelling. With a vector

Basically a direction to the east. But now because she forgot her book we're having her travel west and so notice how initially we travelled 1000 meters 1000 meters away from our initial position. However because we're heading back towards the position we initially came from. We are in a sense subtracting. And so in this case we would say that Dora has travelled a total displacement of zero meters. Why. Because Dora hasn't left her initial position she's moved 0 meters away from where she initially started. Now that we went over briefly about the difference between distance and displacement let's look at the velocity formula. Now normally you may be introduced to the concept of speed and the speed formula and velocity is basically the speed formula. Except we are dealing with vectors so that's the only difference speed does not worry about vectors whereas velocity does worry about vectors and since we're in game programming we do in fact worry about vectors. So a quick look we would say our velocity formula as the following the average velocity is equal to the change in displacement over the change in time.

Again we won't go into a lot of detail in this episode that will be towards the end however the big takeaway I want you is that we can calculate for displacement and so we would say the change in displacement is equal to the average velocity multiplied by the change in time. And so now we have this formula we can work with to calculate our displacement in the game world. Let's go ahead and take a look at acceleration. The formula for acceleration is the following. We would say the Average acceleration is equal to the change In velocity Over the change in time. So the most important takeaway from the acceleration formula is that the change in velocity is equal to the average. Acceleration multiplied by the change in time. Now how exactly do we use these formulas in game programming. How do we use the change in position or a change in displacement. And

And how do we use the change in velocity to help. Us with our game programming journey. It's really simple. You can combine the position. Also known as displacement but I'm gonna keep it as position. And we can change our position in the game world based on velocity multiplied by time and the same thing for velocity. We can change our velocity based on an acceleration multiplied by time. And one important thing to note is that our acceleration must be a. Constant Value. Must be a value that never. Changes. And so from our formula we can actually make A pseudocode for gravity so let's go ahead and take a look at that. Notice how we have a velocity vector 0 0 and a position vector 0 0. Notice how we have an acceleration And The only value we have in our acceleration is nine point eight which is gravity, well gravity is nine point eight one meters per second squared. But we're gonna use the nine point eight value here in our own acceleration formula because we're trying to write pseudocode for graph. And if you look here. Over doing is we're changing our position vector to add on to the lost city multiplied by delta time. Now we haven't gone over delta time. Yet. But. No matter the game engine no matter what game engine you pick. All game engines will provide you with some sort of variable that represents the time in between frames and we're gonna take a look at that later. However

However, The most important thing to notice is that Our position plus equals velocity multiplied by delta time line of code looks almost like our displacement formula that I showed you earlier word displacement was equal to velocity and time. And so as you can see right there we are able to use our velocity formula to help us create a line of code that allows our object in the game world to move. And in this case we're not moving so much as having a force act upon us which is the acceleration and that's the next line of code. Our next line of code is velocity plus equals acceleration multiplied by delta time and the second line of code looks almost like our acceleration formula. Where were we changed the variables for time. We swapped them across the equals sign and we were able to get velocity equals acceleration multiplied by time. And right here in just two lines of code with a basic understanding or not even an understanding just the basic memorization of physics formula we were able to create pseudocode for gravity.