Representation of Different Types of Motion by Simple Graphs

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The Idea

In the previous experiment, we worked with constant velocity in one direction and found that the motion was represented by simple graphs whose slopes were straight lines. Here, you study the motion of a person going forward and back, fast and slow. You also measure the effect of speeding up and slowing down. These graphs will take on a new dimension. In this experiment you use a motion sensor with display software to get a better feel for what different types of motion look like. Graphs are used to show where an object is at various times.

What You Need

• motion sensor
• appropriate computer interface for the motion sensor
• (roughly) 8 inch by 10 inch piece of cardboard

Easy Screen)

1. Attach a motion sensor to your computer. If you have a PASCO motion sensor, it is connected through the computer's USB port by way of a computer interface. Follow the specific details provided by the sensor's manufacturer.
2. If you are using the PASCO sensor, select the Easy Screen to get started. Four motion patterns will come up on the screen. Select one to start with. Press Run (when you are ready).
3. Hold the board facing the motion sensor. (See Figure 2-1.)
4. Position yourself so you start at a distance of 1 meter from the screen. On the computer screen, you see a visual indicator or your position as a function of time.
5. Adjust your position to match the pattern on the screen. (Note: you might be tempted to think that moving forward is positive, but this is not the case here. Moving backward results in increasing the distance between yourself and the motion sensor. As a result, for our purposes here, this is the positive direction.)
6. Repeat for each of the patterns available on the Easy Screen.

Expected Results

Figure 2-2 shows the result of someone moving backward and forward in such a way that they match the target motion pattern. This represents holding still for two seconds at 0.5 meters distance, then moving back at 2.2 m/s, and then holding still for another two seconds at a distance of 1.8 meters. The person doing the matching does not have to think about this, but only needs to look at the screen and move to fit the pattern.

Constant velocity in the positive direction (which in this case is defined as away from the motion sensor) is represented by a straight line on a distance versus time graph. The faster the motion, the steeper the slope.

Zero velocity means the distance stays the same over a given time interval. This is represented as a horizontal line on the distance versus time graph.

A curved line would be produced by accelerated motion (speeding up or slowing down).

Why It Works

The distance an object goes in a given time interval, t, is given by the equation:

From this equation, the slope of the distance versus time graph is given by v, the velocity of the motion. The initial separation from the motion sensor, d°, determines how far above the baseline the graph starts.

Each new phase of the motion contributes a separate segment to the graph. For instance, if the velocity stops, the distance remains constant for that period of time. If the motion is toward the motion sensor for another period of time, that motion contributes a segment of the graph with a negative slope that connects to the other segments.

Table 2-1 summarizes the various possibilities.

A treasure map

1. On a piece of paper, draw the following moves (or make up your own):
• Forward 1 meter in three seconds
• In place four seconds
• Back 0.5 meter in two seconds
• Forward 2.5 meters in four seconds
• In place four seconds
• Back 1 meter in three seconds
2. How far did you get?
• What was your displacement? (This is the total distance you traveled from your starting point.)
• What was the total distance you traveled? Unlike displacement, every forward and backward move contributes to distance.
• What is your overall speed? Your overall speed is the distance divided by the total time. The total time is the same for both of these.

The results of the treasure hunt is:

• Total time = 20 seconds
• Displacement from the starting point = +1 + 0 – 0.5 + 2.5 + 0 – 1 = 2.0 meters
• Average velocity = 2 meters / 20 seconds = 0.1 meters per second
• Overall speed = 4 meters / 20 seconds = 0.2 meters per second

Make your own distance versus time challenges:

1. Select any of the Easy Screen Patterns.
2. Using a transparency marker (erasable or not is your choice) and trace the rectangular shape defining the Easy Screen Graph.
3. Draw your own motion pattern on the transparency.
4. Tape the transparency on the screen, so the rectangle aligns with the one you traced on the screen.
5. Match your pattern by adjusting your distance as before. This time, you will be ignoring the Easy Screen Pattern and following only your own.

Once you get the hang of it, you can throw in accelerated motion. Acceleration (away from the motion sensor) is represented by an upward sloping line, which is curved upward. Acceleration (toward the motion sensor) is represented by a downward sloping line that is curved downward.

The Point

Constant velocity is represented by a straight line on the distance versus time graph. The velocity is given by the slope of the line.

If the curve is not a straight line at any point this indicates that acceleration has occurred. Acceleration can be either positive (speeding up) or negative (called deceleration or slowing down).

An object moving in a particular direction (forward or backward) can experience either positive or negative acceleration.