Chapter 2 Representing Motion

Motion diagram- a series of images that show the position of an object at specific time intervals

Particle model- a simplified version of the motion diagram in which the images are replaced by single points.

When representing motion 2 types of quantities will be used: Scalars- Quantities that describe only size or magnitude, they are just numbers without a specific direction. Examples would be distance 87 km, 23 m, 400 ft Vectors- Quantities that describe both magnitude and direction; examples 87 km east, 23m WSW, 400 ft south  Vectors are represented by arrows that are drawn to scale; When doing a problem involving vectors choose a scale that will produce reasonable vectors (5-10 cm)

N S EW 80 m/s NE 120 m/s SE 66 m/s W Scale 1 cm = 10 m 8 cm 12 cm 6.6 cm

Resultant vectors-the some of 2 or more vectors A boy travels.5 km E to a store to pick up bread and milk. The boy continues.2 km E to deliver the milk and bread to his grandmother. 5 cm2 cm 7 cm What’s the scale? 1cm=.1km How far did the boy travel?.7 km

Time intervals and displacements Two things are used to analyze motion. –Time Intervals- the difference between 2 times Δt= t f - t i Time Interval = final time - initial time –Displacement- the change in position of an object Δd= d f – d i Displacement = final position minus initial position

Distance vs. Displacement Distance and displacement are not necessarily the same thing. –Distance - How far you travel regardless of direction. –Displacement -"Change in position” this not only takes into account distance but direction as well

Example Suppose a person moves in a straight line from the lockers (at a position d i = 1.0 m) toward the physics lab (at position = 9.0 m), as shown below 1.0 m9.0 m Δd= d f – d i = 9.0m – 1.0m = 8.0m

In this example the distance would be described as 8.0 m, but the displacement would be described as 8.0 m to the right Suppose the person turns around! Δd= d f – d i = 1.0m – 9.0m = -8.0m The answer is negative so the person must have been traveling horizontally to the left

What is the DISPLACEMENT for the entire trip? 0 m is the displacement because you have ended at the same spot What is the total DISTANCE for the entire trip? The distance traveled is 16m 8m + 8m= 16m

Position-Time Graphs Graph used to show the position of an object at a specific time. –Y axis- displacement or position –X-axis- time

Where is the object located at 3s? At what point is the object at 7m? What is happening to the object between 6-11s ? What is happening between 11-17s ?

Velocity- the speed of an object in a specific direction; it is a vector quantity because it describes magnitude (how fast) and direction Speed- is simply how fast something is moving; It is a scalar quantity because there is no direction associated with it

Average Velocity Velocity is defined as: “The RATE at which DISPLACEMENT changes”. ddd If you are given a Displacement vs. Time graph, to find the velocity of an object during specific time intervals simply find the slope.

Slope ddd Because velocity is a vector quantity the direction is usually described as being in a positive or negative (backwards) direction

What is the average velocity of the object between 0-6s? 1.7 m/s in a positive direction What is the average velocity of the object between 6-11s? 0 m/s object is stopped What is the average velocity of the object between 15-17s? -1.5 m/s in a negative direction

Average Speed - the average speed of an object does not indicate direction therefore is equal to the absolute value of average velocity Instantaneous velocity – the speed and direction of an object at a specific time. Instantaneous speed – the speed of an object at a specific time

Equations are often more useful than displacement-time graphs; If an object is moving at a constant velocity its graph will be a straight line. y=mx + b d= vt + d i d position/displacement of object v average velocity t time d i initial position