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. |
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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.
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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.) |
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