Unit 2: Constant Velocity Reading 3: Motion...
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©Modeling Instruction – AMTA 2017 1 U2 – Reading 3-v1 + 0 + 0 + 0 Unit 2: Constant Velocity Reading 3: Motion Maps A motion map is a tool for representing the motion of an object by showing the position, velocity, and acceleration of an object at various clock readings. (At this point, you will be representing position and velocity only.) A stroboscopic photograph is a good starting point for thinking about making motion maps. A stroboscopic photograph is a photo that is made with the shutter of the camera open throughout the motion of an object. If the room is dark and the object emits no light, the image formed by the camera will be totally black. If, however, while the shutter of the camera is open, a strobe light flashes at a constant rate, the picture will be different. Now there will be an image of the object formed on the photograph each time the light flashed and produced enough light to capture the image of the object. If the light stays on for only a very short time, and it flashes at a constant rate, the images of the object will be spaced equally in time. If the object is moving in front of the camera, the resulting photo will show the position of the object every time the light flashed. The images on the photo will therefore show the position of the object at equal intervals of time. This makes it quite convenient to describe the motion of the car. To turn the stroboscopic photograph into a motion map, we need to make a few additions. Consider the following stroboscopic photograph of a moving toy truck. The strobe light for this photo was set to flash at 1 flash per second. The resulting images are therefore timed 1 second apart. The object started on the left side of the table and moved to the right. A metric distance scale is included in the photo to allow us to track the position of the car in metric distance units. The first step in making a motion map is to draw a position axis, and to identify which direction you have chosen to call the positive direction. The position axis is being drawn below the stroboscopic photo below. Be sure to label the zero position and to indicate which direction is the positive direction. Having drawn the position axis, the next step in creating a motion map is to make a dot above (or below) the position axis to represent the position of the object at regular time intervals. The truck in this photo had a reflective + taped to it. We will place our dots at the positions of the + on the images of the truck. Finally, having added the dots, you will add arrows to the dots to represent the instantaneous velocity of the object when it is at the position of the dot. The arrows should point in the direction of motion, and should be drawn in proportion to the speed of the object. The result is the completed motion map shown below the strobe photo.
Transcript of Unit 2: Constant Velocity Reading 3: Motion...
©Modeling Instruction – AMTA 2017 1 U2 – Reading 3-v1
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Unit 2: Constant Velocity Reading 3: Motion Maps
A motion map is a tool for representing the motion of an object by showing the position, velocity, and acceleration of an object at various clock readings. (At this point, you will be representing position and velocity only.)
A stroboscopic photograph is a good starting point for thinking about making motion maps. A stroboscopic photograph is a photo that is made with the shutter of the camera open throughout the motion of an object. If the room is dark and the object emits no light, the image formed by the camera will be totally black. If, however, while the shutter of the camera is open, a strobe light flashes at a constant rate, the picture will be different. Now there will be an image of the object formed on the photograph each time the light flashed and produced enough light to capture the image of the object. If the light stays on for only a very short time, and it flashes at a constant rate, the images of the object will be spaced equally in time. If the object is moving in front of the camera, the resulting photo will show the position of the object every time the light flashed. The images on the photo will therefore show the position of the object at equal intervals of time. This makes it quite convenient to describe the motion of the car.
To turn the stroboscopic photograph into a motion map, we need to make a few additions. Consider the following stroboscopic photograph of a moving toy truck. The strobe light for this photo was set to flash at 1 flash per second. The resulting images are therefore timed 1 second apart. The object started on the left side of the table and moved to the right. A metric distance scale is included in the photo to allow us to track the position of the car in metric distance units.
The first step in making a motion map is to draw a position axis, and to identify which direction you
have chosen to call the positive direction. The position axis is being drawn below the stroboscopic photo below. Be sure to label the zero position and to indicate which direction is the positive direction.
Having drawn the position axis, the next step in creating a motion map is to make a dot above (or below)
the position axis to represent the position of the object at regular time intervals. The truck in this photo had a reflective + taped to it. We will place our dots at the positions of the + on the images of the truck.
Finally, having added the dots, you will add arrows to the dots to represent the instantaneous velocity of the object when it is at the position of the dot. The arrows should point in the direction of motion, and should be drawn in proportion to the speed of the object. The result is the completed motion map shown below the strobe photo.
©Modeling Instruction – AMTA 2017 2 U2 – Reading 3-v1
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Below is another strobe photo of a toy truck moving the opposite direction from the one shown on the previous page. The strobe rate is again 1 flash per second. Below the strobe photo is the corresponding motion map. And finally we have another strobe photo of a different toy car moving more slowly to the left. If we were to represent the motion of both toys shown in the strobe photos above on a single position vs. clock reading graph, it would look like the one to the right. The mathematical models for the toy truck and toy car would look like the following:
Throughout this course, we will be representing the behavior of objects in multiple ways including with words, diagrammatically, graphically, and algebraically. Motion maps are an example of a diagrammatic representation of motion. A more complicated motion is represented by the motion map below. Here, an object starts at a position of zero, moves to the right at constant velocity for five seconds, stops and remains in place for two seconds, then moves to the left at a slower constant velocity for three seconds.
Note that there are eleven dots in this motion map. Those eleven dots represent a total time interval of ten seconds. Why are eleven dots, each representing positions at clock readings that are one second apart, necessary to represent a time interval of ten seconds?
©Modeling Instruction – AMTA 2017 3 U2 – Reading 3-v1
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Practice making motion maps by analyzing the position vs. clock reading graphs and creating a corresponding motion map, or by sketching the graph that corresponds to the given motion map
