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## Pixar in a Box

### Unit 7: Lesson 2

The physics of particle systems- Start here!
- Graphing motion over time
- Position, velocity and acceleration
- Vector addition
- Velocity and acceleration vectors
- Understanding net forces
- Net forces
- Force and acceleration
- Applying gravity to a particle
- Particle collisions
- Particle collisions
- Animating particles
- Particle calculations

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# Graphing motion over time

First let's review position, velocity and acceleration vs. time curves.

## Want to join the conversation?

- why do we have to divide?(7 votes)
- It's a rate. A rate represents a ratio, which is better described as a fraction.(4 votes)

- What's the point of knowinng acceleration, if acceleration is constant due to gravity?(0 votes)
- g=9.8 m/s2 is a fact

However, if the particles bounce into each other or get blown away, their acceleration won't be constant anymore. The acceleration may decrease and increase according to other rules of physics ^^(3 votes)

- i dont understand anything(5 votes)
- I'm sorry but what the heck is this? i am heading into high school and i love coding, so far this only consist of graphs. I'm here to code(sorry)(4 votes)
- Why are the effects listed before animation in the content list if you have to reffer to like that?(5 votes)
- Its been organized as best it can be, the small reference in this video was brief and easy to pick up during the course of the video.

Its amazing we even have these in the first place, organization is the least of my concerns.(0 votes)

- I have absolutely no idea what this even means. Can someone please explain this to me in simpler terms?(0 votes)
- This video is just saying that you will learn how to simulate the position, velocity, and acceleration of your particle system. Remember that ball in the video? We are going to be doing the same thing. But first you have to learn how to make it look realistic in the whole animation, which is where you have to learn how to make the position, velocity, and acceleration of your animation/particles look real!(10 votes)

- hey duskpins what is up(2 votes)
- what is a duskpins?(2 votes)

- how old are all the fricking peeps here(2 votes)
- Neither 6 To 10(1 vote)

## Video transcript

- In this lesson, we'll revisit
our ping pong ball simulator but this time from a mathematical or quantitative perspective. By the end of the lesson, you'll learn everything you need to code up your own
ping pong ball simulator and much more. Specifically, we are going to develop mathematical formulas to do three things. One. Describe how particles move based on laws of physics. Two. Control how
particles collide with the walls of the container
and with each other. Three. Create a method
to track particle motion forward in time. To begin to understand how particles move let's draw different kinds of motion. By motion, we mean how
the position of particles will change over time. We got an idea of how things
move in our animation lesson. In that lesson, we animated a ball by drawing it in different
positions over time using each frame indicated
at the bottom of the screen. If we draw the ball
moving an equal distance between each frame, it looks like it's sliding
along a friction-less surface. The speed isn't changing. It's constant. If we plot the position
of the ball over time, we get a straight line. Here, time is expressed
on the horizontal axis and the distance the ball has moved is plotted on the vertical axis. The slope of the line tells us how fast it's moving. A steeper slope means a higher speed. The slope is a change in position divided by the change in time. Now, what if we wanted to plot the ball's speed over time? If the ball speed doesn't change at all, we get a plot like this: A straight horizontal line. A harder challenge is animating the ball so it actually looks like
it is being acted upon by gravity. To do that, we have to
increase the distance that the ball travels between each frame. This is because the ball
needs to speed up as it falls. When we plot the ball's position over time we get a curve. This is because at each
frame we are changing the slope of the line. Now, if we plot the speed
of the ball over time, we get a non-horizontal line. That's telling us that the ball speed is no longer constant. The slope of the line
is telling us how fast the ball's speed is changing. Just like we plotted
the change in position to get the ball speed, we can plot the change in speed to get acceleration of the ball. Here is the plot of
the ball's acceleration versus time. Notice it is a straight line which means the acceleration isn't changing and that's because the acceleration due to gravity is constant. To summarize, speed is
the slope of the ball's position versus time curve. Similarly, acceleration is the slope of the speed versus time curve. As shown in these equations, speed is equal to change in position divided by change in time. And acceleration is
equal to change in speed divided by change in time. But let's pause here. In the next exercise, we'll challenge you to think about how the motion of
objects changes over time in terms of position,
speed and acceleration.