 # Objectives Describe motion in terms of displacement and time.

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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.

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.

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.

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

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

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

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

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

Displacement

Positive or Negative Displacement?

Positive or Negative Displacement?

Positive or Negative Displacement?

Positive or Negative Displacement?

Positive or Negative Displacement?

Positive or Negative Displacement?

Positive and Negative Displacements

Activity: Graphing Position vs. Time
To determine distance and displacement

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

understanding the “distance – displacement" difference

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

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

Average Velocity

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)

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.

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

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.

Sign Conventions for Velocity

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?

Use Dimensional Analysis!
Constant Velocity Use Dimensional Analysis!

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

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

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