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AP Physics 1: Exam Prep12 chapters | 136 lessons

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Lesson Transcript

Instructor:
*Angela Hartsock*

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

In this lesson, we will look at an example of a velocity vs. time graph. By examining the shape of the graph, it is possible to accurately describe the motion of an object, even if that motion is very complex.

First, we used displacement and time to determine velocity, algebraically. We moved on from there to using velocity and time to calculate acceleration, algebraically. Then, we shifted gears and used data points of displacement and time to calculate velocity, graphically. It should come as no surprise that our next step would be to use data points of velocity and time to describe acceleration. So, let's dive in.

At first glance, a graph of velocity vs. time might look a lot like the graphs of position vs. time we've been working with. In fact, they are set up nearly identically. We use the same *x*, *y* coordinate system, the same shape, and the same time variable on the *x* axis. The only difference is instead of position, with the unit meters, on the *y* axis, we use velocity with m/s units. That's the basic velocity vs. time graph.

Remember, what we are describing with these graphs is the motion of an object in a straight line. **Velocity** is a vector quantity, requiring a magnitude and a direction. But, with straight line motion, the only directions we have to worry about are forwards and backwards. When the object is moving forwards, we call it positive. When it's moving backwards, we call it negative and so those values need a negative sign.

You will definitely have to make a velocity vs. time graph for one of your exams, and you should expect to answer several basic questions about the shape of the graph. Fortunately, these graphs are very easy to read, once you understand what's going on. Let's take a look at an example graph representing the motion of a car on a straight track.

As you can see above, we have velocity on the *y* axis and time on the *x* axis. As the car starts moving, the velocity changes from 0 m/s to 20 m/s between *t* = 0 s and *t* = 2 s. Hopefully, you remember that a change in velocity is called acceleration. So, a rising line on a velocity vs. time graph represents that the object is accelerating. Since the velocity is increasing, the acceleration is positive.

Now, look at the graph below between *t* = 2 s and *t* = 6 s. What's going on here? The car is driving at a constant velocity of 20 m/s for 4 seconds. So, a flat, horizontal line means that the velocity is constant and the object is not accelerating.

At the *t* = 6 s mark, the graph turns and starts moving downward. The velocity values are decreasing from 20 m/s at 6 seconds to 10 m/s at 8 seconds as the car applies its brakes. At *t* = 10 seconds, the car stops when the velocity hits 0 m/s. A line moving down towards the *x* axis represents that the object is slowing down. We call this type of motion negative acceleration.

At the *t* = 10 second mark, the line moves below the *x* axis to the point *y* = -10 m/s. During straight line motion, a negative velocity means the object is moving backwards. So, what happened here is that the car is now driving backwards on the track. On a velocity vs. time graph, any time the line crosses the *x* axis, the object is changing direction.

To recap, the car was not moving, then accelerated to 20 m/s before maintaining this speed for 4 seconds. At this point, the car applied its brakes for 4 seconds, negatively accelerating until it stopped. Once stopped, the car reversed direction and accelerated to 10 m/s in the opposite direction.

You could easily describe all that in words but I think it's much easier to simply draw a graph.

Let's briefly review velocity vs. time graphs.

You can determine a lot of information about the straight-line motion of an object by looking at the shape of the line on a velocity vs. time graph. A rising line represents an increase in velocity called acceleration. If the line is flat and horizontal, the object is traveling at a constant speed. A line that is falling towards the *x* axis represents an object that is negatively accelerating, or slowing down. When the line hits the *x* axis, the object has stopped moving. If the graph continues below the *x* axis, the object has changed direction and is moving backwards at increasing velocity.

Following this lesson, you should be able to:

- Define velocity
- Describe how a velocity vs. time graph is set up
- Explain how to determine the straight-line motion of an object using a velocity vs. time graph

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AP Physics 1: Exam Prep12 chapters | 136 lessons

- What is Kinematics? - Studying the Motion of Objects 3:29
- Scalars and Vectors: Definition and Difference 3:23
- What is Position in Physics? - Definition & Examples 4:42
- Distance and Displacement in Physics: Definition and Examples 5:26
- Speed and Velocity: Difference and Examples 7:31
- Acceleration: Definition, Equation and Examples 6:21
- Significant Figures and Scientific Notation 10:12
- Uniformly-Accelerated Motion and the Big Five Kinematics Equations 6:51
- Representing Kinematics with Graphs 3:11
- Ticker Tape Diagrams: Analyzing Motion and Acceleration 4:36
- What are Vector Diagrams? - Definition and Uses 4:20
- Using Position vs. Time Graphs to Describe Motion 4:35
- Determining Slope for Position vs. Time Graphs 6:48
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- Velocity vs. Time: Determining Displacement of an Object 4:22
- Understanding Graphs of Motion: Giving Qualitative Descriptions 5:35
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- Projectile Motion Practice Problems 9:59
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