Back To Course

AP Physics 1: Exam Prep12 chapters | 136 lessons

Watch short & fun videos
**
Start Your Free Trial Today
**

Start Your Free Trial To Continue Watching

As a member, you'll also get unlimited access to over 70,000 lessons in math, English, science, history, and more. Plus, get practice tests, quizzes, and personalized coaching to help you succeed.

Free 5-day trial
Your next lesson will play in
10 seconds

Lesson Transcript

Instructor:
*Angela Hartsock*

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

Distance and displacement might seem like similar terms but in physics, understanding the difference can mean getting a question right instead of wrong. In this lesson, we will define these terms and illustrate how easy it is to confuse the two.

Last Thanksgiving, I decided to run my first 5K. I won't embarrass myself by telling you my exact time, but I was able to successfully finish the race. If you asked the other racers how far I traveled, they would all tell you 5 kilometers. If you asked a group of physicists how far I traveled, they might all tell you 0 kilometers - that I didn't change position at all. It might surprise you to learn that both answers are correct. But how can that be? It all depends on the subtle yet very important difference between distance and displacement.

Let's start by defining these two terms, starting with the easier of the two.

**Distance** is how much ground is covered by an object, regardless of its starting or ending position. There is no directional component to a distance measurement, making it a scalar quantity. So, during my 5K, I ran 5 kilometers total. It doesn't matter where the starting line or finish line were or in which direction I was running. It only matters that, if you trace and measure my path, I covered a distance of 5 km of ground. So, when we asked the other runners how far I had traveled, they all answered correctly with a distance measurement of 5 kilometers.

Let's take a minute to look at our other term: **displacement**, which is an object's change in position considering its starting position and final position. A displacement measurement does not take into account what route the object took to change position, only where it started and where it ended. It is easiest to picture displacement by locating where the object started and drawing a straight arrow from this point to the point where the object stopped moving. Remember, in physics this arrow is called a vector. Its length corresponds to the magnitude, or size, of the movement, and the arrow points in the direction of travel. This makes displacement a vector quantity because it incorporates both movement magnitude and direction.

In the shorthand of physics, displacement is written as *Î”s*. 'Delta' is a Greek letter shaped like a triangle and it's used to represent 'change in.' The 's' stands for spatial location. So *Î”s* stands for a change in spatial location. You should get comfortable using this shorthand just in case you see questions asking for you to solve for *Î”s* that don't actually ask for displacement by name.

Now, before we look at my displacement during my 5K, I want to try and illustrate the concept of displacement. If I walk 3 meters west, then turn and walk 4 meters north, you can easily calculate the distance traveled: 3 m + 4 m = 7 meters. Since this is a distance, there is no need to worry about the direction of travel. Now, let's determine my displacement. I can draw an arrow that starts where I started walking and extends to the point where I stopped walking. It should look like this, forming a right triangle. To determine my displacement, all I need to do is determine how long the arrow is using the lengths of the sides and the Pythagorean Theorem.

*a*^2 + *b*^2 = *c*^2

Since *c*^2 is your displacement squared, it should be written as (*Î”s*)^2.

*Î”s* = âˆš{(3*3) + (4*4)}

*Î”s* = âˆš(9 + 16)

*Î”s* = 5 meters northwest

Doing the math yields a value of 5 meters. But this is not the displacement. Remember, we need a direction as well. In this case, I ended up northwest of where I started, so my displacement is 5 meters northwest. Notice that I traveled a total distance of 7 m but have only a displacement of 5 meters northwest.

Now back to my 5K. You might already be able to figure out what's going on here. How can I travel a distance of 5 km but have a displacement of 0? The trick here is that the race route was a big circle; the starting line and finish line were at the same place. So if we draw out the race route and track my progress around the circle, you can see that I did run 5 kilometers around the race route. But try to draw a vector directly connecting my starting position and my ending position without taking into account my route. You only have one point, so you can't draw a vector. So, my displacement was 0.

Let's quickly review distance and displacement.

**Distance** is how much ground is covered by an object regardless of its starting or ending position. In order to determine distance traveled, you must measure the length of the entire path taken by the object. If you run a 5K on a circular course, your distance traveled is 5 kilometers, regardless of where you started and finished. Distance is a scalar quantity.

**Displacement** is an object's change in position, only measuring from its starting position to the final position. Displacement only takes into account your position change from the start to the end, not the exact path you took to get there. To calculate displacement, simply draw a vector from your starting point to your final position and solve for the length of this line. If your starting and ending position are the same, like your circular 5K route, then your displacement is 0. In physics, displacement is represented by *Î”s*.

By completing this lesson, you might strengthen your capacity to:

- Compare distance and displacement, and distinguish between the two
- Recall the meaning of
*Î”s* - Calculate displacement

To unlock this lesson you must be a Study.com Member.

Create
your account

Already a member? Log In

BackDid you know… We have over 95 college courses that prepare you to earn credit by exam that is accepted by over 2,000 colleges and universities. You can test out of the first two years of college and save thousands off your degree. Anyone can earn credit-by-exam regardless of age or education level.

To learn more, visit our Earning Credit Page

Not sure what college you want to attend yet? Study.com has thousands of articles about every imaginable degree, area of study and career path that can help you find the school that's right for you.

You are viewing lesson
Lesson
4 in chapter 3 of the course:

Back To Course

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
- 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
- Using Velocity vs. Time Graphs to Describe Motion 4:52
- 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
- Go to AP Physics 1: Kinematics

- Drama 101: Intro to Dramatic Art
- Team Briefing Basics for Supervisors
- Communications 104: Intro to Mass Communications I
- Art 104: History of Western Art II
- Inclusion in Recruitment, Interviews & Hiring
- Origins of Theatre
- Western Theatre from Renaissance to Realism
- Theatre as Activism
- Introduction to the Dramatic Arts
- Contemporary Theatre
- Study.com FTCE Scholarship: Application Form & Information
- Study.com CLEP Scholarship: Application Form & Information
- List of FTCE Tests
- CLEP Prep Product Comparison
- CLEP Exam vs. AP Test: Difficulty & Differences
- CLEP Tests for the Military
- How to Transfer CLEP Credits

- Dislocated Ribs: Symptoms & Treatment
- What is Air Resistance? - Lesson for Kids
- The IRAC Method
- What is an Absolute Phrase? - Definition & Example
- Interaction of Major Systems & Processes in Plants
- Federal & State Regulation of Healthcare Organizations & Providers
- Constructed Textiles Designers
- Linear vs. Branched Silanes
- Quiz & Worksheet - Themes in Dracula
- Quiz & Worksheet - Subsequent Events on Balance Sheets
- Quiz & Worksheet - I/O Psych Data Collection
- Quiz & Worksheet - Noise Pollution Causes & Examples
- Quiz & Worksheet - Efficiency, Equity & Voice in Business
- How to Cite Sources Flashcards
- Evaluating Sources for Research Flashcards

- 10th Grade English: Credit Recovery
- 11th Grade English: Credit Recovery
- Prentice Hall Biology: Online Textbook Help
- DSST Criminal Justice: Study Guide & Test Prep
- Middle School US History: Homework Help Resource
- Post-War World (1946-1959) Lesson Plans
- Sampling in Psychological Research Lesson Plans
- Quiz & Worksheet - Commonly Used Veterinary Forms
- Quiz & Worksheet - Appeal to Force Fallacy
- Quiz & Worksheet - Characteristics of Intrinsic Renal Failure
- Quiz & Worksheet - Effects of Calcium Levels in the Blood
- Quiz & Worksheet - Immune Hemolytic Anemia

- Major Trends & Developments in International Business
- Methods for Assessing Students' Prior Knowledge & Skills
- Dividing Fractions Lesson Plan
- Dividing Fractions Lesson Plan
- How to Ace the ACT
- Bible Study Topics
- 2nd Grade Reading List
- The Fall of the House of Usher Lesson Plan
- AP English Literature & Composition Reading List
- What Are AP Exam Pass Rates?
- Columbus Day Activities for Kids
- What's the Common Core Framework?

Browse by subject