Learn

Distance and Displacement

As you know, there are many different aspects of motion. For this lesson, we are going to focus on two aspects, and we will continue to add to these aspects as we move through the unit. In this lesson we will focus on distance and displacement.

Distance

Distance is the total length traveled. In measuring distance, it does not really matter what direction the travel is in, just the total amount of distance covered.

For example, Forrest walks:

  • 12 meters
  • Turns left and walks 10 meters
  • Turns right and walks 4 meters
  • Then stops.

To find the total distance Forest traveled, we just add up all the different lengths he walked:

12 m + 10 m + 4 m = 26 meters

The total distance total length traveled is 26 m.

You can make this into a formula if that helps:

dT= d1 + d2

  • dT is the total distance traveled.
  • d1 and d2 are the different distances traveled in the problem (and there can be d3 or d4 or more depending on the problem)

So in the problem above

  • d1 = 12 m
  • d2 = 11 m
  • d3 = 4 m
  • So dT =12m +11m + 4 m, which is 26 m.

Now you try one.
Sally:
  • Walks 16 m east
  • Turns and walks 3 m west
  • Then turns again and walks 5 m south

What is the total distance Sally walked?

Displacement

Displacement is similar to distance but with one very important difference — displacement takes into account the direction of the motion.

  • Displacement is the change in position of an object.
  • This means that displacement can be either positive or negative, depending on which direction the object moves.
  • Displacement is not always equal to distance.

Think about this example:

  • I leave my house and walk around my block, which is a total of 35 m.
  • At the end I return to the exact point (my house) that I began.
  • What was my distance total length traveled and my displacement change in position?

Well, figuring out the distance is easy. I walked 35 m around the block so my distance traveled is 35 m.

Displacement may not be quite as easy to see. Remember, displacement is change in position. In the question, I began and ended at the same position (my house) so my displacement is 0 m.

The formula for finding displacement is:

Change in position = final position — initial position

Δx = xf - xi

In this formula:

  • Δ = The change in position (the delta symbol, or Δ, means “change in”)
  • xf = final position
  • xi = initial position

Displacement can be either positive or negative and is not always the distance traveled. The initial position(xi) and final position (xf) are the start and the end of any interval you choose. The direction can be indicated by a plus or minus sign.

When the displacement is in the same direction, you add like (or same) units. For example, if someone travels 5 m east and then 4 meters east, his displacement would be 9 m (5 m east + 4 m east = 9 m east). In this case, because the different parts of the motion were both in the same direction (east), we were able to just add them together — which also means the displacement was the same as the distance.

When the motion is not all in the same direction, you must compare your values or your directions. If they are in opposite directions, you will need to subtract. For example, a girl on a bicycle:

  • Rides 9 m east
  • Turns around
  • Then rides 3 m west

What is her displacement?

Well, if she went 9 meters east but then came back west for 3 meters, she really only changed position by 6 meters. Therefore, her displacement is 6 m east (9 m east - 3 m west = 6 m east).

Visit the Physics Classroom to learn more about distance and displacement.