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TExES Physics/Mathematics 7-12 (243): Practice & Study Guide62 chapters | 688 lessons | 60 flashcard sets

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Lesson Transcript

Instructor:
*David Wood*

David has taught Honors Physics, AP Physics, IB Physics and general science courses. He has a Masters in Education, and a Bachelors in Physics.

After completing this lesson, you will be able to explain what free fall motion is, and identify and draw displacement, velocity, and acceleration-time graphs for free fall motion.

**Free fall motion** is the motion of an object under only the force of gravity. If any other force is affecting the object, it isn't considered to be free fall.

Before we talk about that motion in more detail, let's go over some key terms you should know to understand this lesson. **Displacement**, otherwise known as position, is where you are located related to the origin (usually where you started). **Velocity** is how fast you're moving in a particular direction, or in other words, it's the rate at which your displacement is changing. And **acceleration** is how quickly your velocity is changing. If your velocity is constant, your acceleration is zero, but if you're speeding up or slowing down, then you are accelerating. An acceleration of 4 meters per second squared means that your velocity is changing by 4 meters per second every second.

When an object falls downwards under gravity, it accelerates at a rate of 9.8 meters per second squared downwards on average at the surface of the Earth. It doesn't matter if the object is huge or tiny, heavy or light. All objects in free fall on Earth fall at the same rate. This number is called the acceleration due to gravity, and varies by your position relative to the center of the Earth. It gets a little weaker as you move further away, but not that much. Even on the international space station, gravity is almost as strong at about 8.7 meters per second squared.

Some physicists would define free fall motion as motion at that particular acceleration. When you do that, it means that even throwing a ball upwards is free fall. Once it leaves your hand, its velocity might be upwards, but it still has an acceleration of 9.8 meters per second squared downwards. That's why it slows down, stops, and falls back to Earth.

Graphs of free fall motion are really important ones to know. They're always the same shape (as long as we ignore air resistance), and they're pretty distinctive. There are two main sets of graphs: graphs for an object that has been dropped, falling to Earth, and graphs for an object that is thrown upwards. For this lesson, we'll combine those two together. We're going to talk about the graphs for an object thrown upwards that then falls back down to Earth. If you can draw a graph for this complete motion, you can draw a graph for anything.

The three most useful graphs to describe motion are displacement-time, velocity-time and acceleration-time graphs. So let's look at each of these in turn.

A **displacement-time graph** of the motion would look like this:

It's a curve because the object is accelerating; it's changing speed. It starts off going super fast as it leaves your hand, so the position changes rapidly. Then it stops in place at the top of its motion for an instant. Finally, it falls back down, slowly at first, but getting faster and faster. This graph is perfectly symmetrical, which tells you that when it gets back to your hand, it's going just as fast as when you threw it.

A **velocity-time graph** of the motion would look like this:

Since the object is moving up at first, the velocity starts out as positive (up is usually called positive). It reaches a velocity of zero at the top of its path for a moment; that's when the line crosses the x-axis. Then as it falls back down, its velocity is negative. The velocity changes in a consistent way because the acceleration is constant.

Another way to think about this graph is that it represents the slope of the displacement-time graph. The slope of the displacement graph starts out positive and steep, flattens off to zero, and then becomes negative and steep. The velocity therefore starts out positive, decreases to zero, and then becomes negative.

An **acceleration-time graph** of the motion would look like this:

Pretty simple; just a constant acceleration of negative 9.8 meters per second squared. It's negative because gravity acts downwards (the acceleration is pointed down). Again, this could be seen as the slope of the velocity-time graph. That graph had a constant, negative slope. So we have a constant, negative acceleration.

If you ever need graphs for an object that is dropped and is simply falling, all you have to do is only draw the second half of the graphs. And that's it; that's all you need to know about the graphs of free fall motion.

**Free fall motion** is the motion of an object under only the force of gravity. If any other force is affecting the object, it isn't considered to be free fall. When an object falls downwards under gravity, it accelerates at a rate of 9.8 meters per second squared downwards on average at the surface of the Earth. It doesn't matter if the object is huge or tiny, heavy or light. The graphs of free fall motion for an object thrown upwards, from the time its released until the time it returns to your hand, look like this:

The slope of the displacement-time graph gives you the velocity, and the slope of the velocity-time graph gives you the acceleration.

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TExES Physics/Mathematics 7-12 (243): Practice & Study Guide62 chapters | 688 lessons | 60 flashcard sets

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