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**Objectives Describe motion in terms of displacement and time.**

Calculate the displacement of an object Construct and interpret graphs of position versus time.

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**One Dimensional Motion**

To simplify the concept of motion, we will first consider motion that takes place in one direction. One example is the motion of a commuter train on a straight track.

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**Distance and Displacement**

In physics we distinguish between the length of the trip (distance) and the direct distance between the starting point and ending point (displacement) Distance – (scalar) – “how much ground an object has covered” during its motion Displacement – (vector) – “how far out of place an object is”; it is the object’s change of position and its direction.

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**Distance Displacement**

The length an object actually travels. How far you go. Scalar Displacement The change in position of an object. Length between start and finish Vector

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**Scalar Vector a quantity fully described by only a magnitude**

i.e. 5m; 20°C Vector a quantity fully described by both a magnitude and direction. i.e. 30 m/s, East; 5 mile, North

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**Displacement Displacement is a change in position.**

Displacement is not always equal to the distance traveled. The SI unit of displacement is the meter, m Of course we know this

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Motion Example: A man walks 4m East, 2m South, 4m West and then 2m North. 4 m Distance traveled = 12m Displacement = 0m 2 m 2 m 4 m

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**displacement = final position – initial position**

Dx = xf – xi displacement = final position – initial position 8

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Displacement

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**Positive or Negative Displacement?**

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**Positive or Negative Displacement?**

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**Positive or Negative Displacement?**

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**Positive or Negative Displacement?**

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**Positive or Negative Displacement?**

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**Positive or Negative Displacement?**

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**Positive and Negative Displacements**

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**Activity: Graphing Position vs. Time **

To determine distance and displacement

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**displacement = final position – initial position**

Dx = xf – xi displacement = final position – initial position 18

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**understanding the “distance – displacement" difference**

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Average Velocity Average velocity is the total displacement divided by the time interval during which the displacement occurred.

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Average Velocity In SI, the unit of velocity is meters per second, abbreviated as m/s. 21

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Average Velocity

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Velocity vs. Speed Velocity describes motion with both a direction and a numerical value (i.e. magnitude). (vector) Speed has no direction, only magnitude. Average speed is equal to the total distance traveled divided by the time interval. (scalar)

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**Interpreting Velocity Graphically**

For any position-time graph, we can determine the average velocity by drawing a straight line between any two points on the graph. If the velocity is constant, the graph of position versus time is a straight line. The slope indicates the velocity.

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**Interpreting Velocity Graphically**

Object 1: positive slope = positive velocity Object 2: zero slope= zero velocity Object 3: negative slope = negative velocity 25

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**Interpreting Velocity Graphically**

The instantaneous velocity is the velocity of an object at some instant or at a specific point in the object’s path. The instantaneous velocity at a given time can be determined by measuring the slope of the line that is tangent to that point on the position-versus-time graph.

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**Sign Conventions for Velocity**

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Constant Velocity The fastest fish, the sailfish, can swim 1.2 × 102 km/h. Suppose you have a friend who lives on an island 16 km away from the shore. If you send a message using a sailfish as a messenger, how long will it take for the message to reach your friend?

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**Use Dimensional Analysis!**

Constant Velocity Use Dimensional Analysis!

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The peregrine falcon is the fastest of flying birds (and, as a matter of fact, is the fastest living creature). A falcon can fly 1730 m downward in 25 s. What is the average velocity of a peregrine falcon? 30

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In the Netherlands, there is an annual ice-skating race called the “Tour of the Eleven Towns.” The total distance of the course is 2.00 × 102 km, and the record time for covering it is 5 h and 40 min. Calculate the average speed of the record race in km/h. 31

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**The Sears Tower in Chicago is 443 m tall**

The Sears Tower in Chicago is 443 m tall. Joe wants to set the world’s stair climbing record and runs all the way to the roof of the tower. If Joe’s average upward speed is 0.60 m/s, how long will it take Joe to climb from street level to the roof of the Sears Tower? 32

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