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AP Physics 1: Exam Prep13 chapters | 143 lessons | 6 flashcard sets

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Lesson Transcript

Instructor:
*Angela Hartsock*

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

Simply looking at a position vs. time graph can tell you a lot about straight line motion, but doing a few basic calculations can tell you even more. In this lesson, we will learn how to use the slope of the line to determine average velocity.

Learning physics is a lot like playing with blocks. Before you can build a tower, you need to make a solid base. Before you describe the motion of the planets, you need to start with something simpler and describe the motion of a car driving along a straight road.

In another lesson, we discussed graphing the position versus the time for an object in motion. Now it's time to add another layer of knowledge and learn how this graph can be used to calculate the average velocity of your moving object.

In algebra class, probably about the time you were introduced to the *x*-*y* scatter graph, you not only learned how to plot data points, but you learned how to calculate the slope of the line as well. The **slope** is defined as the change in *y* divided by the change in *x*. Let's write this a slightly different way.

Slope = Î”*y* / Î”*x*

Remember, the triangular symbol delta (Î”) means 'change in.'

But let's look at our graph. On a position vs. time graph, *y* is position, which we can also call displacement (represented by the letter *s*). Displacement has the unit meters. *x* is time (represented by the letter *t*) and has the unit seconds. Let's substitute these values into our equation:

Slope = Î”*s* / Î”*t*

Does this equation look familiar? It should. This is the equation for calculating average velocity.

Average Velocity = Î”*s* / Î”*t*

Need a bit more convincing? The units for displacement are meters (m). The units for time are seconds (s). So, displacement divided by time gives an answer with meters per second (m/s) as units, the exact units attached to average velocity.

This was a very long-winded attempt on my part to tell you that the slope of a position vs. time graph gives you the velocity of the object in motion. Hopefully, by laying it out this way, it'll stick in your brain.

There is one quick point to be made here: velocity is a vector quantity. This means that there must be a directional component. Since we are only graphing objects traveling in a straight line, the only two directions we need to be concerned with are forwards and backwards. If the velocity has a positive sign, the object must be moving forwards. If the velocity has a negative sign, the object is moving backwards.

Let's look at a position vs. time graph so we can practice calculating the average velocity. First, let's determine the average velocity between 0 and 3 seconds.

Average Velocity = Î”*s* / Î”*t*

The easy variable to calculate is Î”*t*. The question asks for the change in displacement between 0 and 3 seconds, so 3 seconds - 0 seconds = a change in time of 3 seconds. Now, simply follow the 3 second grid line up to where it intersects the blue graph line.

Then, once you hit the intersection, if you read across to the position axis, you can see that this occurs at the 30 meter mark. Since the object started at the 0 meter mark, the change in position is 30 meters - 0 meters, which equals 30 meters. Now simply plug these values into the equation:

Average Velocity = Î”*s* / Î”*t* = 30 m / 3 s = 10 m/s

The average velocity over the first 3 seconds of the graph is 10 m/s.

We can also determine the average velocity over the entire portion of the graph. The last point on our graph is at -15 meters and 17 seconds. Remember, this is a vector quantity, so the total distance traveled is not important, only the displacement from the starting position, which is 0 meters at 0 seconds in this problem.

According to the graph, we're -15 meters from the starting position, and it took us 17 seconds to get there. Plugging these numbers into the average velocity equation, we have:

Average Velocity = Î”*s* / Î”*t* = -15 m / 17 s = - 0.88 m/s

The average velocity over the entire graph is -0.88 m/s. The negative value indicates that, overall, the object moved backwards from where it started.

We can also determine the average speed of our object, which is the total distance traveled divided by the total time it took to travel that distance. The equation looks like this:

Average Speed = Î”*d* / Î”*t*

In the speed equation, the letter *d* represents the total distance traveled. The object moves forward 30 meters, then back 15 meters, then back 30 meters for a total of 75 meters. Since speed is a scalar quantity, there is no negative sign associated with any of these values.

Total Distance Traveled = 30 m + 15 m + 30 m = 75 m

Filling in the equation:

Average Speed = Î”*d* / Î”*t* = 75 m / 17 s = 4.4 m/s

Always remember to double-check the question to be sure what it's asking for. In this case, the average velocity and average speed were dramatically different.

Let's review. A position vs. time graph can be used to represent the motion of an object on a straight path. You can calculate the slope of a line on a graph with the following equation:

Slope = Î”*y* / Î”*x*

Substituting the appropriate values in for the variables yields the following equation, which can be used to calculate the average velocity of the object:

Average Velocity = Î”*s* / Î”*t*

The units for velocity are m/s. Remember that velocity is a vector quantity dependent on the displacement from the starting position only, not the total distance traveled. A positive velocity means the motion was forwards, and a negative velocity means the motion was backwards.

These graphs can also be used to calculate average speed with the following equation:

Average Speed = Î”*d* / Î”*t*

Average speed takes into account the total distance traveled and does not have a directional component attached to it.

Following this lesson, you'll be able to:

- Describe the purpose of a position vs. time graph
- Identify the equations for slope, average velocity and average speed
- Explain how a position vs. time graph can be used to calculate average velocity and average speed

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AP Physics 1: Exam Prep13 chapters | 143 lessons | 6 flashcard sets

- 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
- Determining Acceleration Using the Slope of a Velocity vs. Time Graph 5:07
- Velocity vs. Time: Determining Displacement of an Object 4:22
- Understanding Graphs of Motion: Giving Qualitative Descriptions 5:35
- Free Fall Physics Practice Problems 8:16
- Graphing Free Fall Motion: Showing Acceleration 5:24
- The Acceleration of Gravity: Definition & Formula 6:06
- Projectile Motion: Definition and Examples 4:58
- Projectile Motion Practice Problems 9:59
- Kinematic Equations List: Calculating Motion 5:41
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