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### Course: Mechanics (Essentials) - Class 11th > Unit 4

Lesson 1: How far do we really go at the end of the day? Exploring the difference between distance and displacement.# Distance and displacement in one dimension

Using a one-dimensional number line to visualize and calculate distance and displacement. Created by Sal Khan.

## Want to join the conversation?

- first thank you very much for creating these videos for us. I'm currently in physical science but i've always wanted to learn physics. also i want to ask is all of this going to get any harder than it is right now?(17 votes)
- Oh yeah bud. More complex and more interesting, too.(19 votes)

- How does the lemon move?(8 votes)
- Although this is unnecessary to the actual problem, a lemon can move in many ways, for example, having someone move it. However, it is extremely important to state that a lemon is an arbitrary object, and its being a lemon does not affect the way it moves. Thank you.(18 votes)

- So like in one dimension or on a number line we have 2 directions right(+) or left(-) so if he says 2 to the left it means -2. But in a 3dimension world, we have 4 directions North, South, East, and West.

It was hard to understand!(4 votes)- Hey azlan,

Think of a dimension in the sense of the Cartesian coordinate system. With it, you can use the same number of values (x, y, z) as dimensions. Each dimension can be represented by another axis, orthogonal (perpendicular) to every other.

With a 1D world, you can define any point on the line with 1 value. In a 2D world, you'll need 2. This is the familiar Cartesian grid system you know and love from math class. You can have positive and negative values on both axes, so you have four directions. In a 3D world, you need 3 coordinate points, and thus you have six "directions": North, East, South, West, up, and down.

Hope this helps,

Hunter(11 votes)

- what is symbol of distance and displacement ?(3 votes)
- Distance is denoted by "d" while most of the books use "x" or "s" for displacement(9 votes)

- What is net displacement? Thanks.(4 votes)
- It is s=vt or displacement equals velocity multiplied by time.(4 votes)

- Displacement Sum of all vectors

Distance Sum of the Absolute value of all vectors

Is this another way to define the difference?(3 votes)- Distance is the actual path travelled in a given time interval.

Displacement is the difference between the initial and final point of an object at a given time interval.(7 votes)

- Isn't the absolute value of distance travelled always make it positive?(2 votes)
- Yup, that seems pretty right.

Since distance itself is a scalar, with no direction, negative and positive never take place in the value. No left or right.

So it will always be positive.(4 votes)

- Why is it called net displacement?(0 votes)
- It is called net displacement because it is the overall change in position. You would get this by subtracting the initial position from the final position.(4 votes)

- In my textbook , distance is denoted by the letter 's' so is it wrong ?(2 votes)
- no cuz its just a placeholder-some use s, some d, some x...(3 votes)

- What is different distance and displaysment(2 votes)
- Distance is the total amount an object has traveled which is a scalar (only has magnitude but not direction) quantity and it's always a non-negative number and displacement is the change in position of an object and its a vector quantity (has direction and magnitude).(3 votes)

## Video transcript

- [Instructor] Previous videos we've talked a little bit
about distance traveled versus displacement. What I'm gonna do in
this video is discuss it on a one dimensional number line. And we'll get a little bit
more mathy in this video. So here is my number line. Let's say that this is a zero, one, two three, four and it keeps going on and then in the negative direction, negative one, negative two, and negative three. And let's say that I start off with a lemon. Let's say my lemon starts
off right over here at zero on my number line. And let's say it first
moves two to the right so at first moves two to the right. I'll denote that by plus two and then from there, it moves three to the left and then it moves three to the left. And I will use negative for the left. So it moves three to the left. And then let's say that it then moves another one to the left. So then it goes another one to the left and I'll denote negative one as moving one to the left. So based on what we know
about distance traveled and displacement, what is the distance
traveled for this dot? Distance traveled. Pause the video and see if you can figure that out. Or remember, distance traveled is
the entire path length. Or the entire length of the dot's journey. So this is going to be equal to two to the right. So plus two and then three to the left. Now this is an important notion. When we talk about distances, we wouldn't say positive or negative. We just care about the absolute value of the amount that we are traveling. So we won't specify a direction. Now you might say, "hey, "where is the direction being specified?" well implicitly, whether
something is positive or negative on this number line is giving a direction. But if we're talking about distances, we wouldn't pay attention
to the direction. We only care about the magnitude. So this would be two plus three plus one. Doesn't matter if this is one to the left or one to the right. Doesn't even matter if it's
positive one or negative one. We care about its absolute value. We care about its magnitude. So the distance traveled in this example is going to be six units. Whatever the units are on my
number line right over here. If these are in meters then this would be six meters. Now what is the displacement? Now remember, displacement
is net change in position. Displacement. What is that going to be? Pause the video and see
if you can figure it out. Well displacement is going to be you could view this as equal to your final position and we'll use X. Let's say this is the X-axis. So we'll say X final, your final position minus your initial position. It's really just your change in position! So what is your change in position here? Well your final position is you are at negative two
at x equals negative two. And then what was your initial position? Your initial position,
you started at zero. So negative two minus zero
is equal to negative two. So how would we visualize
that on our drawing here? Well we started here. Just think about what is
your net change in position? You started here. And regardless of what your path was, you ended up two to the left. So your your displacement is negative two. Now displacement, we care not just about the magnitude. We care about the magnitude
and the direction. So you might be saying, well, where is the direction specified if I just say negative two? Well, the sign in a one dimensional case is giving us our direction. So the sign is giving us a direction. I started off implicitly with this notion that negative is to the left and positive is to the right. And we're in this one dimensional world. And those are the only two
directions that I can travel in. So if I'm in this one dimensional world or if I'm thinking about
just one dimension, the sign gives me my direction. So that's why displacement where I care about the
magnitude and the direction, I do care about the sign. While distance, where I only care about the magnitude, I don't care about the sign. So I just keep adding up the magnitudes while over here, another
way you can think about it, you first get displaced
by two to the right so that's plus two. The plus says to the right. Then you get displaced
by three to the left. So that is minus three. And then you get displaced
by one to the left again. So that's minus one. That's why we're talking
about displacement. That's why we care about the sign. And if you are to add
all of these together, you are going to get a net displacement of negative two. But an easier way was just
what's your final position minus your initial position?