You can just look at graphs of straight line motion and accurately describe how that object is moving. In this lesson, we will investigate the basic shapes the graphs can take and what conclusions you can draw from these shapes.
No Math Today
For some of you out there, I have some good news. This kinematics lesson will not include any numbers or math. At this point, you should know how to perform all the necessary calculations with Position vs. Time and Velocity vs. Time graphs. Now, we're going to see what we can figure out just by looking at the shapes of these graphs, no numbers required.
If I show you two different Position vs. Time graphs and ask you to tell me which one represents an object traveling at a constant velocity, you should have no problem figuring it out.
After all, this graph shows the position and the time both changing at a constant rate. The second graph shows an object that is not moving. If you had to, you could calculate the slopes of the graphs and give me the velocity. But, what if I take away all the numbers? Can you still pick out the graph of constant velocity? Of course you can. The graph still shows the position and time changing at a consistent rate even though I've taken away the actual values.
What you've just done is make a qualitative assessment of the graph and used it to describe the motion of the object. With qualitative graphing you are describing the motion of an object by recognizing the basic shapes on its graph, not through exact calculations.
The best way to proceed is to look at the seven basic shapes of Velocity vs. Time and Position vs. Time graphs. By the end, you should be able to quickly recognize what's going on in each graph, what a specific type of motion looks like on both types of graphs, and how to sketch one type of graph if given the other type. Let's dive right in.
Basic Graph Shapes
1: The object is not moving.
As you can see, the position is not changing on the first graph, and the velocity is 0 m/s on the second. Here, you are simply standing still.
2: The object is moving at a constant velocity in the positive direction.
Here, position and time are changing at a constant rate, upwards. The velocity graph is horizontal, above the time axis. Now, you are walking a steady pace forward.
3: The object is moving at a constant velocity in the negative direction.
These graphs are the opposite of #2. Position is constantly changing downward. Velocity is a horizontal line below the time axis. Back at the starting point, you decide to walk backwards at a steady pace.
4: The object is speeding up (or accelerating) in the positive direction.
The Position vs. Time graph shows an object that is moving faster as time passes, drawn as a curve. The velocity graph is increasing constantly, in a straight line. A steady speed won't cut it anymore. You start walking slowly but steadily move faster until you're running forward.
5: The object is slowing down in the positive direction.
These graphs show the opposite of #4. The change in position decreases as time passes. The velocity steadily decreases. This time, you are already running forward at the start but gradually slow down to a stop.
6: The object is slowing down in the negative direction.
This one can be a bit harder to grasp. Position is changing backwards, towards the starting point and the overall speed is getting slower. For me, this is easier to see on the velocity graph. The velocity is decreasing towards 0 m/s. Since the graph is below the time axis, the vector is negative, meaning the object is moving backwards. Starting several meters away from the fixed starting point, you sprint backwards towards it. You can't sprint for long and gradually start to slow down until you stop moving.
7: The object is speeding up in the negative direction.
These graphs are the opposite of #6. Position is changing backwards faster as time passes. Again, for me this is easier to see on the velocity graph. The velocity is increasing, but since the line is below the time axis, the velocity is increasing in the negative direction. Again, several meters from the original fixed starting point, you decide to head back. This time you start walking but speed up to a run as you head backwards.
Let's review. Kinematics can be represented visually using graphs. Velocity vs. Time and Position vs. Time graphs are the most common. Once you get familiar with these graphs, you can begin to pick out trends without using numbers or doing any math. Qualitative observations rely on your ability to pick out these basic shapes and use them to describe the motion of the object being graphed.
There are seven basic shapes you should become familiar with. I recommend looking at many graphs until you feel comfortable with every possible combination of motion.
Study this lesson's details in order to enhance your capacity to:
- Make qualitative observations by looking at graphs
- Describe the seven basic shapes of graphs that you should be familiar with