# Download e-book Introduction to motion

Over the years, scientists have discovered several rules or laws that explain motion and the causes of changes in motion.

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There are also special laws when you reach the speed of light or when physicists look at very small things like atoms. Speed it Up, Slow it Down The physics of motion is all about forces. Forces need to act upon an object to get it moving, or to change its motion.

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Changes in motion won't just happen on their own. So how is all of this motion measured? Physicists use some basic terms when they look at motion. How fast an object moves, its speed or Velocity , can be influenced by forces. Note: Even though the terms 'speed' and 'velocity' are often used at the same time, they actually have different meanings. Acceleration is a twist on the idea of velocity.

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Acceleration is a measure of how much the velocity of an object changes in a certain time usually in one second. Velocities could either increase or decrease over time. Mass is another big idea in motion. Mass is the amount of something there is, and is measured in grams or kilograms.

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A car has a greater mass than a baseball. Simple and Complex Movement There are two main ideas when you study mechanics. The first idea is that there are simple movements , such as if you're moving in a straight line, or if two objects are moving towards each other in a straight line. The simplest movement would be objects moving at constant velocity. Slightly more complicated studies would look at objects that speed up or slow down, where forces have to be acting. Video transcript - [Instructor] What we're going to do in this video is start to think about how we describe position in one dimension as a function of time.

So we could say our position, and we're gonna think about position on the x-axis as a function of time. And we could define it by some expression, let's say, in this situation, it is going to be our time to the third power minus three times our time squared plus five. And this is going to apply for our time being non-negative 'cause the idea of negative time, at least for now, is a bit strange. So let's think about what this right over here is describing.

And to help us do that, we could set up a little bit of a table to understand that depending on what time we are, let's say that time is in seconds, what is going to be our position along our x-axis?

So at time equals zero, x of zero is just going to be five. At time one, you're gonna have one minus three plus five. So that is going to be, let's see, one minus three is negative two, plus five is going to be, we're going to be at position three.

And then at time two, we are going to be at eight minus 12 plus five, so we're going to be at position one. And then at time t equals three, it's gonna be 27 minus 27 plus five, we're gonna be back at five. And so, this can at least help us understand what's going on for the first three seconds.

So let me draw our positive x-axis. So, say it looks something like that. And this is x equals zero.

## One-dimensional motion

This is our x-axis. X equals one, two, three, four, and five. And now let's play out how this particle that's being described is moving along the x-axis. So we're gonna start here, and we're gonna go one, two, three. Let's do it again.

We're going to go one, two, three, the way I just moved my mouse, if we assume that I got the time roughly right, is how that particle would move. And we can graph this as well. So for example, it would look like this. We are starting at time t equals zero. Our position, this is our vertical axis, our y-axis, but we're just saying y is going to be equal to our position along the x-axis. So that's a little bit counterintuitive because we're talking about our position in the left-right dimension, and here you're seeing it start off in the vertical dimension, but you see the same thing.

At time t equals one, our position has gone down to three. Then it goes down further. At time equals two, our position is down to one. And then, we switch direction and then over the next, if we say that time is in seconds, over the next second, we get back to five. Now an interesting thing to think about in the context of calculus is, well, what is our velocity at any point in time? And velocity as you might remember, is the derivative of position. So let me write that down. So we're gonna be thinking about velocity as a function of time.

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And you could view velocity as the first derivative of position with respect to time which is just going to be equal to, or we're gonna apply the power rule and some derivative properties multiple times. If this is unfamiliar to you, I encourage you to review it. But this is going to be three t squared minus six t and then plus zero, and we're gonna restrict the domain as well for t is greater than or equal to zero. And then, we can plot that. It would look like that. Now let's see if this curve makes intuitive sense.

We mentioned that one second, two seconds, three seconds. So we're starting moving to the left.