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Lesson

Drawing Linear Motion Diagrams

- To learn the terms in Kinematics
- To be able to draw a motion diagram that represents the motion as described in a kinematics problem.

- The kinematics quantities can be related as:
- Position (x) - the location of an object.
- Average velocity(v)- the change in position divided by the change in time (sometimes called the rate of change of position of the object), and
- Average acceleration(a)- the change in velocity divided by the change in time (sometimes called
the rate of change of velocity of the object).

- One of the tools that can be used to help visualize and understand motion is the motiondiagram. There is no elaborate art involved here; it is simply a sketch. The moving object can be represented by a dot. The motion diagram shows the position of the object as it moves over time. There is equal time between each object position in the diagram below.
You can think of it as a stroboscopic picture. (A stroboscope is a light source that flashes on and off periodically.) Imagine that the object is in the dark, except for the strobe. Every time the light flashes on, you can see the object’s position. The time between flashes is always the same, and the path of the motion will be recorded.

This represents a motion diagram for a car moving to the right. The diagram starts at time = 0 s, when the car is at position 3 m. It continues at regular time intervals, until the car is at position 11 m.

- Procedurein more detail… Now you add the various types of motion.
- To draw a motion diagram, you want to sketch 3 to 5 consecutive “frames” of the position of the object. This would by done by drawing the actual object at some initial position. Then, you would draw a second object at its next position (next frame). For example, if the object is moving to the right, then the next position would be to the right. How much to the right depends on how fast the object is moving – greater separation of the two objects if the object is moving fast, smaller separation of the two objects if the object is moving slow. You would follow this same approach for the next 2 to 4 frames.
- To draw the velocity “arrows”, you look at the separation between two consecutive objects (this is the rate of change in position) and draw the length of the velocity arrow (called the velocity magnitude or speed) based on the position separation. The direction of the velocity arrow is in the direction that the object is moving. We locate the velocity arrow usually below the drawn object at the same location below the drawn object.
- To draw the acceleration “arrow” (only one arrow for constant acceleration motion diagrams), you look at the separation between the velocity arrows (this is the rate of change in velocity). If the velocity arrows are not changing length and direction, then the acceleration is zero. If the velocity arrows are getting longer, then the acceleration is some constant in the same direction as the velocity arrows. If the velocity arrows are getting shorter, then the acceleration is some constant in the opposite direction to the velocity arrows.

Constant Velocity:

The direction of the acceleration arrow is in the same direction as the velocity arrows since the speed is increasing.

- This implies that the acceleration is in the opposite direction to the direction of the velocity.

- This is only part of the motion diagram necessary to solve this problem. What about the initial motion of the camera still moving up after the camera is dropped.
- This is only after the camera stops moving upward and is only falling downward.

1-dimensional kinematics of a body undergoing constant acceleration. Includes visually integrating the acceleration and velocity graphs, and visually differentiating the position and velocity graphs.