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**GRAPHICAL ANALYSIS OF MOTION**

Chapter 2.3 GRAPHICAL ANALYSIS OF MOTION 1

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**Describe the following motion**

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**from the graph to an actual motion and **

In Kinematic, when you work on a graph analysis problem you must translate: from the graph to an actual motion and from an actual motion to its representation on a graph. 3

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**Objective Solve “slope of a curve” with unit a graph.**

Identify direction of motion from a graph Transfer a position vs. time graph to velocity vs. time graph. Solve “area under a curve” with right unit Solve displacement and distance from speed vs. time graph. 4

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**Example: a line drawn at 45° always has a slope of 1 (no units), **

“slope of a curve” Students don’t recognize that a slope has units or how to determine those units. Example: a line drawn at 45° always has a slope of 1 (no units), Position vs. time graph, slope is a velocity and unit is [m/s] 5

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When the velocity is constant, the average velocity is equal to the instantaneous velocity at any time. 6

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a. x Object starts at the origin and moves in the positive direction with constant velocity. t Object starts to the right of the origin and moves in the negative direction with constant velocity ending at the origin. x b. t 7

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**Object moving to the right at a fast constant speed.**

A qualitative description of the motion depicted in the following v-versus-t graphs: a. v Object moving to the right at a fast constant speed. t b. v Object moving to the left at a slow constant speed. t

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**Object starts to the right of **

x Object starts to the right of the origin and moves in the positive direction with constant velocity. t x d. Object starts to the left of the origin and moves in the positive direction with constant velocity ending at the origin. t 9

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**Object starts to the left of the origin and moves in **

x Object starts to the left of the origin and moves in the negative direction with constant velocity. t x f. Object starts to the right of the origin and moves in the negative direction with constant velocity. t 10

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v t Object starts at R of origin. Moves R at constant v, stands still then moves L at faster constant v.

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**Object moves L at constant v, then **

x t Object moves L at constant v, then moves R at constant v but slower, then stands still. 12

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**• Students don’t recognize that an “area under the curve” **

Area under a curve • Students don’t recognize that an “area under the curve” has units or how the units of an “area” can be something other than area units. The area under the v-versus-t curve is displacement. But distance is a length? How can a length equal an area? 13

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The students should be able to calculate the area under the v-t curve and understand that the value obtained is the displacement 14

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**Object starts at R of origin. Moves L at constant v, stands still then **

moves L again at constant v but faster. 15

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**then moves L at constant v but slower.**

x v t Object is at rest. Moves R at constant v, then moves L at constant v but slower. 16

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**Practice: find displacement**

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**Practice: find displacement**

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INTERPRETING GRAPHS Give a qualitative description of the motion at the different time intervals. v (m/s) t (s)

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INTERPRETING GRAPHS Give a qualitative description of the motion at the different time intervals. Stops, Resting, speeding up + direction Slowing down + direction, speeding up - direction, Slowing down - direction, Constant speed + direction, constant speed - direction v (m/s) t (s)

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**Motion diagram and Position vs, Time graph**

Look at the following motion diagram Transfer this motion into position vs. time graph. What is mathematical equation of this graph?

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