11

Describing Motion

Displacement and DistanceChapter 2

22How do You Describe Motion?

• Use a Frame of Reference – A system of objects that are not moving with respect with each other.

• Reference Point – The zero point for your system, what you make your measurements from.

• Think about it:– If you were just floating in space could you tell you were

moving if you couldn’t see anything else?

Answer: No, it would be impossible. You might be able to tell if you were speeding up or down but not now fast you were moving, if you were moving or in what direction.

*All Motion is Relative to some reference

33

Who is Moving Where?

The girl sees the boy moving to the right

The boy sees the girl moving to the left

Which is correct?

It is all a matter of what frame of reference you use.

44

• The most commonly used frame of Reference is the

surface of the Earth.

55

66

77

88

• Earth rotates on its axis at 1,100 mph

• Earth orbits the Sun at 67,000 mph

99

• The whole galaxy rotates at 480,000 mph

So how fast are you going?

It’s all relative

1010So How Fast are You Really Moving?

Earth rotates at 1100 miles / hr

You

Earth revolve around the Sun at 30 km / sec or 67,000 miles / hr

Our solar system revolves around the galaxy at 220 km / sec or 490,000 miles / hr

225 million years to make one (1) rotation around the galaxy

You

The Milky Way relative to other galaxies moves at 1,300,000 miles / hr

1111

Most all Physics quantities can be described as either a

vector or scalar

How Much How Much & in Which Direction

1212

Scalar

• A quantity that takes one piece of information to describe

• In Physics, a quantity that consists of a magnitude or amount only (number and units)

• Examples – distance, speed, liters,

1313

Vectors• A number that takes two pieces of

information to describe

• In Physics, this is a magnitude (scalar) and a direction of action

– Direction can be – Positive (+) or negative (-)– Up, down, left or right– N, S ,E or W– Degree or angle heading

• Examples – displacement, velocity, acceleration, force

1414Distance v.s. Displacement• Distance

– The total length of the path taken.

– Scalar

– Always positive

– Measured in meters (m), kilometers (km), or centimeters (cm)

• Displacement – The difference between the

final position and the initial position

– Or, how far from the starting point in a straight line and what direction

– Vector

– May be positive or negative

– Measured in meters (m), kilometers (km), or centimeters (cm)

1515An Ant Takes a Trip

Which represents the ants distance traveled?

Blue path

Which represents the ants displacement?

Red Path

When can displacement and distance traveled be the same?

If you travel in a straight line.

1616

Speed and Velocity

Chapter 2

1717

Speed• The rate at which something is moving.

• The ratio of how far something moves to the time it takes to move

– Scalar

– Always positive

– Measured in meters/second (m/s) or kilometers/hour (km/hr)

Average speed = distance traveled total time t

d

1818

Equation for Speed

v = speed

d = distance

t = time

td

dt

td

1919Velocity

• How fast an object is moving in a particular direction

Describes both rate and direction• The ratio of an objects displacement to the

time it takes to be displaced.– Vector

– Can be positive or negative

– Measured in meters/second (m/s) or kilometers/hour (km/hr)

Average velocity = displacement total time t

d

2020Farmer Jones drives 6 miles east down a straight road. She turns around and drives 4 miles back. What was her average

speed and velocity for this trip if it took 1 hour?

Speed = ?1st Distance = 6mi + 4mi

= 10 miles

2nd Speed = distance time = 10 miles 1 hr = 10 miles/hr

Velocity = ?1st Displacement = 6mi - 4mi

= 2 miles [east]

2nd Velocity = displacement time = 2 miles [east] 1 hr = 2 miles/hr [east]

Q: Why is Ms. Jones’ speed and velocity different for her trip?A: She changed direction, backtracked for part of her trip.

Knowns: 1st leg = 6 mi [east] 2nd leg = 4 mi [west] t = 1 hr

2121

Example ProblemA toy train moves along a

circular path of radius 20 cm as shown in Fig. 2-3.

What is the distance and displacement traveled when the train(a) moves from O to P? (b) moves from O to P and then back to O?

Answer: (a) distance: 62.8 cm,

displacement: 40 cm, to the North;

b) distance: 126 cm, displacement: 0 cm. rC 2