Angela has taught college Microbiology and has a doctoral degree in Microbiology.
Describing motion with graphs can be a simple, yet powerful tool in your physics arsenal. In this lesson, we begin by looking at the basic position vs. time graph.
Graph It Instead
Motion can be quite variable. Think about the last trip you took in your car. I'm sure you got in the car while it was stopped, it changed position as you drove down the street, stopped again at a red light, and continued changing position when the light turned green. If we wanted to study the change in position using kinematics and algebra, you would need to make a long list of all the changes in position and how long it took you to make those changes. What you would end up with is a long list of numbers. Let me suggest a more streamlined approach. Let's just make it a graph.
Position Versus Time Graph
I'm sure you know that driving in your car encompasses all the basic components of kinematics: position, displacement, velocity, time, and acceleration. To get more comfortable working with kinematics graphically, let's focus only on position and time for now. We are also going to assume that the object is moving in a straight line and can only go forwards and backwards.
The best way to start is to set up our graph. Start with a basic grid, and draw in the x and y axes. Time, on the horizontal axis, only needs positive values. Our graph of the motion starts when we get in the car. This is when we start our timer, and since we can't go backwards in time, we don't need negative seconds. Position, on the vertical axis, does need negative values, which we'll get to in a minute. Always fill in the numbers on the axes and add the arrows on the ends. Hopefully your graph looks like this:
Position vs. time graph
Now, I'm going to plot some points that represent a car in motion, and we'll see if we can figure out what exactly that car did. The first point we see below is at 0 meters and 0 seconds. This is the time and position where the car started. If you follow the line, the car moved 15 meters in 2 seconds. Between 2 and 6 seconds, the line is flat, meaning the car must be stopped. Time is still increasing but the car is stuck at the 15 meter mark, possibly stopped at a red light. From 6 seconds to 9 seconds, the car moves again, this time traveling 10 meters.
Graph for example
Okay, so that means in the first 9 seconds, the car has moved 25 meters in the same direction. At the 9 second mark, the line turns and begins moving down. This represents a change in direction. The car has now turned around and is heading back where it came from. During the 4 seconds between 9 and 13 seconds on the graph, the car travels 25 meters back to where it started. Between 13 and 14 seconds, the car is motionless again. Finally, the car drives 10 meters beyond the start point (0 seconds, 0 meters) in 2 seconds.
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You can see how the graph is able to relay all of this information in one compact figure. There is no need to do math, adding and subtracting meters and seconds to determine how far the object traveled and how fast it got there. This simple graph told you everything you needed to know about the motion of the object.
You'll no doubt see problems that involve this type of graph. Here is just one example of questions you could see. By understanding how to read the graph, you should be able to easily answer anything thrown at you.
Look at the graph below of position vs. time. Describe what is happening at the 7 seconds point?
Graph for example problem
The line approaching 7 seconds is moving up. This means the object is moving forward and getting farther from its initial position. At 7 seconds, the line reverses direction and is moving down. This means object has turned around and is moving backwards towards its initial position. At 7 seconds, there is a change in direction of the object.
Now, describe what is happening between 9 and 13 seconds.
During this time period, the object is not moving. Its position is 10 meters from its initial position throughout the 4 seconds period. It's not moving forwards or backwards.
Position vs. time graphs can be a great way to pack all the information describing the motion of an object into one figure. If we set up our graph with position on the y-axis and time on the x-axis, a line on the graph that is rising represents motion away from the object's initial position. A line that is moving horizontal represents that the object has stopped moving. And a line that is moving downward represents that the object is moving backwards towards the initial position.
After you have finished with this lesson, you'll be able to:
Describe how position vs. time graphs can help you easily solve kinematics problems
Explain how to read a position vs. time graph while solving a sample problem
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