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 cm 2 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= tf - ti

Time Interval = final time - initial time

– Displacement- the change in position of an object Δd= df – di

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 di = 1.0 m) toward the physics lab (at position = 9.0 m) , as shown below

1.0 m 9.0 m

Δd= df – di = 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= df – di = 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 VelocityVelocity is defined as: “The RATE at which DISPLACEMENT changes”.

d d d

If you are given a Displacementvs. Time graph, to find the velocity of an object during specific timeintervals simply find the slope.

Slope

d d d

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 + di

d position/displacement of object v average velocity t time di initial position