In this lab you will examine two different ways that the motion of an object that moves along a line can be represented graphically.
You will plot position–time and velocity–time graphs of the motion of the IOLab, a computer-interfaced device that is able to accurately measure the motion of its wheels. The study of motion and its mathematical and graphical representations is known as kinematics.
The purpose of this investigation is to learn how to relate graphs of the distance as a function of time to the motions they represent. You will need the following materials:
How does the distance–time graph look when you move the IOLab slowly? Quickly? What happens when you move the IOLab to the right? To the left? After completing this investigation, you should be able to look at a distance–time graph and describe the motion of an object. You should also be able to look at the motion of an object and sketch a graph representing that motion.
WARNING: Never click the Restart button by mistake.
Clicking this button will cause the IOLab to save your work and go back to the beginning.
If you do click Restart, follow the instructions about the IOLab given to you to
retrieve your saved work and start again.
NOTE: The IOLab and software afford you the opportunity to repeat measurements very quickly. Get into the habit of repeating your measurements until you get a clear representation of what you are exploring.
7. Repeat the steps to graph the following: Faster motion to the right. Be sure to collect the data for the entire 5 s.
8. Repeat this a couple of times, to make sure you captured a good example of moving at a constant speed to the right. (Use +Add Run to collect a new graph, and Remove to remove the graphs you don't want. Be sure to keep the graph from the previous activity - moving slowly to the right.)
Question 1-1: Describe the difference between a graph made by moving the IOLab slowly to the right at a constant speed and the one made by moving it quickly to the right.
9. Repeat the steps to graph the following: Slow motion to the left. Keep the front of the IOLab (+y) pointing to the right, and collect data for the entire 5 s.
10. Repeat this a couple of times, to make sure you captured a good example of moving at a constant speed to the left. (Again use +Add Run to collect a new graph, and Remove to remove the graphs you don't want. Be sure to keep the graph from the previous two activities.)
11. Repeat the steps to graph the following: Faster motion to the left. Again keep the front of the IOLab (+y) pointing to the right, and collect data for the entire 5 s.
12. Repeat this a couple of times, to make sure you captured a good example of moving at a constant speed to the left.
Question 1-2: Describe the difference between a graph made by moving the IOLab to the left and the one made by moving it to the right.
Prediction 1-1: Select from the graphs below your prediction for the position-time graph of the IOLab starting at the origin, moving it slowly and steadily to the right for 5 s, stopping for 5 s, and then moving it back to the origin twice as fast.
Test your prediction.
Question 1-3: Is your prediction the same as the result? If not, then describe how you would move the IOLab to make a graph that looks like your prediction.
By now you should be pretty good at predicting the shape of a position–time graph of the moving IOLab. Can you do things the other way around by reading a position–time graph and figuring out how to move the IOLab to reproduce it? In this activity you will move the IOLab to match a given position-time graph.
Question 1-4: What was the difference in the way you moved the IOLab to produce the two differently sloped portions of the graph you just matched?
Question 1-5A: Describe how you must move the IOLab to produce this position–time graph
Question 1-5B: Describe how you must move the IOLab to produce this position–time graph
Question 1-5C: Describe how you must move the IOLab to produce this position–time graph
Question 1-6: What is the general difference between motions that result in a straight-line position–time graph and those that result in a curved-line position–time graph?
You have already plotted the position of the IOLab as a function of time. Another way to represent the motion of the IOLab is with a graph that describes how fast and in what direction it is moving. This is a velocity–time graph. Velocity is the rate of change of position with respect to time. It is a quantity that takes into account the speed (how fast the IOLab is moving) and also the direction it is moving. Thus, when you examine the motion of an object moving along a line, the direction the object is moving is indicated by the sign (positive or negative) of the velocity.
Graphs of velocity over time are more challenging to create and interpret than those for position. A good way to learn to interpret them is to create and examine velocity–time graphs of the IOLab, as you will do in this investigation.
Question 2-1: What is the most important difference between the graph made by moving the IOLab to the right slowly and the one made by moving it to the right more quickly?
Question 2-2: How are the velocity–time graphs different for motion to the right and motion to the left?
Prediction 2-1: Select from the graphs below your prediction for the velocity-time graph of a more complicated IOLab motion. Begin with the IOLab at the origin:
Test your prediction. Click Record to begin graphing, and repeat the motion of the IOLab until you think it matches the description:
Be sure to collect data for the entire 10 s.
Question 2-3: Which velocity vector above best represents the following motion described
Question 2-3A: Moving slowly to the right
Question 2-3B: Remaining still (Hint: How long is the velocity vector?)
Question 2-3C: Moving rapidly to the left
In this activity, you will try to move the IOLab to match a velocity–time graph shown on the axes on the right. This is often much harder than matching a position graph as you did in the Activity 1-2. Most people find it quite a challenge to move the IOLab so as to match a velocity graph. In fact, some velocity graphs that can be invented cannot be matched!
Prediction 2-2: Describe in words how you would move the IOLab so that its velocity matched each part of this velocity–time graph. Be precise in your predictions. Include how fast the IOLab should move.
Prediction 2-2A: 0 to 4 s:
Prediction 2-2B: 4 to 8 s:
Prediction 2-2C: 8 to 12 s:
Prediction 2-2D: 12 to 18 s:
Prediction 2-2E: 18 to 20 s:
Click Record to begin graphing, and move the IOLab so as to imitate this graph the best you can. (Note, you won't be able to exactly duplicate this graph ) Be sure to collect data for the entire 20 s. You may try a number of times. Get the times right. Get the velocities right.
Question 2-3: Describe how you moved the IOLab to match each part of the graph. Did this agree with your predictions?
Question 2-4: Is it possible for an object to move so that it produces an absolutely vertical line on a velocity–time graph? Explain. Is it possible to duplicate the sharp corners on the graph? if not, why not?
Question 2-5: Did the IOLab pass through the origin on your return trip? If so, why did this happen?
Question 2-6: Does a velocity graph tell you where the motion of the IOLab started--where the origin is? Explain.
You have looked at position–time and velocity–time graphs separately. Since position–time and velocity–time graphs are different ways to represent the same motion, it is possible to figure out the velocity at which the IOLab is moving by examining its position–time graph. Conversely, you can also figure out how far someone has traveled (change in position) from a velocity–time graph.
Prediction 3-1: Predict a velocity graph from a position graph. Carefully study the position–time graph on the axes above and select the velocity–time graph below that would result from the motion.
Question 3-1: How would the position graph be different if you moved the IOLab faster? Slower?
Question 3-2: Did the velocity-time graph agree with your prediction? Explain.
Question 3-3: How would the velocity graph be different if you moved the IOLab faster? Slower?
Prediction 3-2: Predict a position graph from a velocity graph. Carefully study the velocity–time graph on the axes below and select the position–time graph below that would result from the motion. (Assume that the IOLab started at the origin.)
Question 3-4: How can you tell from a velocity–time graph that the moving object has changed direction?
Question 3-5: Did the position-time graph agree with your prediction? Explain.
Question 3-6: How can you tell from a position–time graph that an object’s motion is steady (motion at a constant velocity)?
Question 3-7: How can you tell from a velocity–time graph that an object’s motion is steady (constant velocity)?
Please remember to edit the report (insert your name - and if necessary your partners), export the report and submit it on D2L.
Now do the homework associated with this lab.