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**Picturing Motion Describing Motion with Diagrams …. . . . . . . . . . .**

Ticker Tapes Vector Diagrams

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Ticker Tapes A common way of analyzing the motion of objects in physics labs is to perform a ticker tape analysis. A long tape is attached to a moving object and threaded through a device that places a tick upon the tape at regular intervals of time – say every 0.1 second. As the object moves, it drags the tape through the "ticker," thus leaving a trail of dots. The trail of dots provides a history of the object's motion and is therefore a representation of the object's motion. The distance between dots on a ticker tape represents the object's position change during that time interval. A large distance between dots indicates that the object was moving fast during that time interval. A small distance between dots means the object was moving slow during that time interval. Ticker tapes for a fast-moving and a slow-moving object are depicted below.

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The analysis of a ticker tape diagram will also reveal if the object is moving with a constant velocity or with a changing velocity (accelerating). A changing distance between dots indicates a changing velocity and thus an acceleration. A constant distance between dots represents a constant velocity and therefore no acceleration. Ticker tapes for objects moving with a constant velocity and an accelerated motion are shown below.

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Vector Diagrams Vector diagrams are diagrams which use vector arrows to depict the direction and relative magnitude of a vector quantity. Vector diagrams can be used to describe the velocity of a moving object during its motion. For example, the velocity of a car moving down the road could be represented by a vector diagram. In a vector diagram, the magnitude of the vector is represented by the size of the vector arrow. If the size of the arrow in each consecutive frame of the vector diagram is the same, then the magnitude of that vector is constant.

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**The diagrams below depict the velocity of a car during its motion**

The diagrams below depict the velocity of a car during its motion. In the top diagram, the size of the velocity vector is constant, so the diagram is depicting a motion of constant velocity. In the bottom diagram, the size of the velocity vector is increasing, so the diagram is depicting a motion with increasing velocity – i.e., an acceleration.

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**Accelerated Motion Looking at GRAPHS!**

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**Review Position vs. Time Graph**

What is happening in each graph in your own words?

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**Nonuniform Motion - Changing Velocity**

Position vs. Time Graph Velocity vs. Time Graph Nonuniform Motion - Changing Velocity Position vs. Time Graph Velocity vs. Time Graph Q: What does the slope on a Position vs. Time Graph tell us? Q: What does the slope on a Velocity vs. Time Graph tell us? A: The slope on a Position vs. Time Graph tells us the velocity. A positive slope indicates a positive velocity. A negative slope indicates a negative velocity. A: The slope of a velocity vs. time graph tells us the acceleration. A positive slope indicates a positive acceleration. A negative slope indicates a negative acceleration.

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**Now: Let’s look at a Position vs**

Now: Let’s look at a Position vs. Time Graphs more carefully before we get deeper into Velocity-Time Graphs….

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**From A to B: From B to C: From C to D:**

LET’S LOOK AT A FULL TRIP…. The following graph shows Melissa’s trip to the store. Explain what is happening in each interval of the Position-Time Graph. (Assume she starts at home.) Hint: Always define the initial and final velocities QUESTIONS: When is Melissa moving with A POSITIVE velocity? A NEGATIVE velocity? In which interval is Melissa moving with the greatest velocity? In which period is she moving the slowest? Does she ever change direction? If so, when? How do you know? P O S I T N Figure 1. Position-Time Graph for a complete trip. From A to B: From B to C: From C to D: From D to E: From E to F:

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**Constant Rightward Velocity**

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**Constant Leftward Velocity**

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**Rightward Velocity with Rightward Acceleration**

Pos Velocity + Pos Accel Rightward Velocity with Leftward Acceleration Pos Velocity + Neg Accel

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**Leftward Velocity with Leftward Acceleration**

Neg Velocity + Neg Accel Leftward Velocity with Rightward Acceleration Neg Velocity + Pos Accel

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