# Graphing Free Fall Motion: Showing Acceleration

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• 0:01 Advantages of Studying…
• 0:42 Free Fall Basics
• 1:51 Position vs. Time Graph
• 3:23 Velocity vs. Time Graph
• 4:32 Lesson Summary
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Lesson Transcript
Instructor: Angela Hartsock

Angela has taught college Microbiology and has a doctoral degree in Microbiology.

Kinematics topics are great for using x, y scatter graphs to visualize motion. In this lesson, we will examine the basic shapes of two different types of graphs of an object in free fall.

## Advantages of Studying Free Fall

Objects in free fall are a great tool to use while studying kinematics: we finally have a real world example of straight line motion with constant acceleration. Even better, we finally have a system we can experiment with. You can take everyday objects like tennis balls, drop them from different heights, and time how long it takes to hit the ground. Using these times and knowing the acceleration due to gravity, you should be able to calculate all kinds of information, like displacement and velocity. But there's something else you can do if you have displacement, velocity, and time values. You can plot those values on position vs. time and velocity vs. time graphs.

## Free Fall Basics

Before we dive into what these graphs of free fall motion will look like, I wanna take a minute to do a quick refresher. Free fall describes any motion involving a dropped object that is only acted on by gravity and no other forces. Remember, with free fall we have to ignore any impacts of air resistance on the object. We're only concerned with the acceleration due to gravity, which is a constant value of -9.8 m/s^2 and represented by a lower-case g.

Acceleration is a vector quantity, so it must have a magnitude and a direction. In the case of gravity, the force always acts downward on the object, forcing it towards the ground. Since your exam will generally consider anything in the upwards direction to be positive and anything in the downward direction to be negative, the vector direction of acceleration due to gravity must be negative. Since it must be negative, it needs a negative sign. Of course, you are free to assign your own vector directions, but if you consistently use up as positive and down as negative, you can help reduce any potential confusion or errors later. It'll help to keep this point in mind when we start looking at graphs.

## Position vs. Time Graph

To start, let's take our tennis ball, raise it up ten meters, and drop it. What happens? The ball starts at rest, begins to speed up after you release it, and continues to accelerate at a constant rate of 9.8 m/s^2 until it hits the ground. In other words, the tennis ball is accelerating in the negative direction because down is always considered negative.

So what does this look like on the position vs. time graph? This is a basic position vs. time graph:

The first point on our graph starts at the red arrow above: time = 0 seconds and position = 10 meters. As we start the clock, the position decreases as the ball falls, but the object is speeding up so position must change faster as time passes. What you end up with is a graph that looks like this:

It starts high on the y axis and curves down toward the x axis.

You may have noticed that I didn't include any values for time in seconds or position in meters on this graph. The reason is that if you plot the position over time of an object in free fall that starts high off the ground and motionless, it will always look like the graph above. It doesn't matter if you drop the ball from one meter or ten meters or 10,000 meters. The graph will always have this basic shape: a negative parabolic curve.

You can also graph the motion of objects that are thrown upwards or start on the ground and travel up before falling back down, but these details are not important for this lesson. All you need to do here is recognize this basic shape on a position vs. time graph.

## Velocity vs. Time Graph

We can also graph free fall on a velocity vs. time graph, like this one:

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