Show Menu

Distance, Displacement, and Position Cheat Sheet (DRAFT) by

A physics cheat sheet explaining the difference between distance and displacement and how to calculate them.

This is a draft cheat sheet. It is a work in progress and is not finished yet.

Distance and Displa­cement

Put simply, distance is the total amount something traveled (measured in centim­eters, meters, or kilome­ters) and displa­cement is only how far away it ended from its starting point (simpifies to XF - XI, or final position minus initial position.)
Distance and displa­cement are NOT the same thing, and most problems later on in physics will be asking you about displa­cement. Make sure you know which one you're looking for!

Average Speed vs. Average Velocity

Average speed is the total distance traveled divided by the total time traveled over a certain interval. Speed is a scalar measur­ement, which means it has no direction, only a magnitude.

Average velocity is the total displa­cement traveled divided by the total time traveled over a certain interval. Velocity is a vector measur­ement, which means it has a magnitude and a direction. It is often written as Δx / Δt, or change in position over change in time.

Slope And Its Meanings

On a position vs. time graph:
Positive slope
Object moving forward
line going up slowly
object moving forward slowly
line going up quickly
object moving forward quickly
Negative slope
Object moving backward
line going down slowly
object moving backward slowly
line going down quickly
object moving backward quickly
Zero slope
Object not moving
To find velocity from a graph like this, find the total displa­cement over the time traveled during the interval.

Special Cases

If an object stops in the exact same place it starts (for example, it travels in a circle or a square), the displa­cement is 0. Remember, the displa­cement is only the difference between the final position and the initial position, so if they are the same point, there is no differ­ence.
If the distance is a straight line, the displa­cement and the distance will be the same.

Interp­reting Position vs. Time Graphs

A position vs. time graph will have position on the y-axis and time on the x-axis. These graphs can be used to find instan­taneous speed (the speed the object is going at a specific time) and average speed (about how fast the object was going overall).

Remember that position is measured in m and time is measured in s, so this graph is describing changes in m/s. Since you know that m/s is the unit for velocity, you know that the line is really showing changes in velocity.

Interp­reting Velocity vs. Time Graphs

In a velocity vs. time graph, velocity will be plotted on the y-axis and time will be plotted on the x-axis. Remember that velocity is measured in m/s and time is measured in s; therefore, this graph truly shows us a changes in m/s2. This means that the graph is really describing a change in accele­ration.

Example Problems

Andrew drives 7 kilometers north, then drives 5 kilometers east. What distance did he cover? What was his displa­cement?

When solving for distance, we can just add the 7 km and the 5 km because distance looks for the total kilometers she traveled.

When solving for displa­cement we need to find how far away from his starting point he ended. To find this, make a straight line from the beginning point to the end point. This will create a triangle, and then you can use a2 + b2 = c2 to solve for c, which will be the displa­cement.

So, the answers to this problem:
Distance: 12 km
Displa­cement: √74 km, or about 8.6 km.

Tips and Tricks

Note: Having graph paper can be extremely helpful when dealing with distance problems. (For problems like these, it's okay to give your answer in the same unit you're given.)