Graphing Position & Speed vs Time: Practice Problems

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  • 0:02 What Are Position & Speed?
  • 1:21 Graphing Position & Speed
  • 2:14 Practice Problems
  • 3:42 Lesson Summary
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Lesson Transcript
Instructor: David Wood

David has taught Honors Physics, AP Physics, IB Physics and general science courses. He has a Masters in Education, and a Bachelors in Physics.

After watching this video, you should be able to explain what position and speed are. You should also be able to plot position vs. time and speed vs. time graphs. A short quiz will follow.

What Are Position and Speed?

Position is your current location in space, measured relative to some reference point. Maybe your position is 3 miles west of the lighthouse or 2 miles from the center of Chicago.

Distance is the amount of space between two things or people, measured as a continuous line. We measure distance in units like miles, kilometers, meters, centimeters, inches and yards. Distance traveled is related to your change in position, but it isn't quite the same thing.

Your position is where you are, at a particular moment, and if your position changes by 5 meters, then you have traveled a distance of at least 5 meters. But they're still not the same thing. Maybe while you were changing position by 5 meters, you took the long, scenic route. You still ended up 5 meters from where you started, but you traveled a greater distance.

If you know the time it took you to travel a distance, or the time it took you to change position, you can figure out your speed. Speed is the rate at which your position changes, measured in meters per second, or miles per hour, or similar. Your speed tells you how many meters you travel each second, or how many miles you travel each hour. A speed of 50 miles per hour means that your distance is changing at a rate that would mean you traveled 50 miles every hour.

Graphing Position and Speed

We can create graphs of position and speed, if we know how they changed over time.

A position vs. time graph is a graph with position on the vertical (y) axis and time on the horizontal (x) axis. It tells you how the position of an object changed over a period of time. For example, in Graph 1 a bicyclist cycles from the origin to a position of 4 meters away from the origin, stays where she is for a little while, and then cycles back to her starting position again.

Position vs. Time Graph

A speed vs. time graph is a graph with speed on the vertical (y) axis and time on the horizontal (x) axis. It tells you how the speed of an object changed over a period of time. For example, Graph 2 is the speed vs. time graph of the bicyclist. She moved at one speed at first, stopped for a while, and then went back towards the origin at a slower speed.

Speed vs. Time Graph

Practice Problems

Now it's time to practice making some position vs. time and speed vs. time graphs.

Practice Problem 1: A car travels 30 miles in 1 hour, stops in a car park for 1 hour, and then travels 90 miles in 2 hours. Plot a position vs. time graph of the motion.

Get some graph paper, a ruler and a pencil, and have a go at drawing the graph.

If you've already had a go at plotting the graph, you'll want to see the answer. Your graph should look like Graph 3, below. It slopes up as the car travels 30 miles in the first hour, goes flat as the car stays at the same position for the next hour, and then the car travels even further (another 90 miles) for the last 2 hours.

Graph for Practice Problem 1

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