UNIT 2

MOTION

SECTION 3 - VELOCITY

How fast do you think we are traveling (orbiting) around the sun?

67,0672 mph

How fast do you think we are spinning around our axis as we move around the sun?

1,041.67 mph

Why don’t we feel this motion?

Question!?!?

To describe motion accurately, a frame of reference is

necessary.

Frame of Reference is a system of objects that are not moving

with respect to one another

Frame of Reference

Motion is a change in position relative to a frame of reference

Relative Motion

Movement in the relation to a frame of reference

Frame of Reference

The speed of the passenger with respect to the ground

depends on the relative directions of the passenger’s and

train’s speeds:

16.2 m/s 13.8 m/s

Example:

A passenger is seated on a bus that is traveling with a velocity

of 6 m/s east. If the passenger remains in her seat, what is her

velocity:

a) With respect to the ground?

b) With respect to the bus?

c) The passenger decides to approach the driver with a velocity

of 1 m/s. What is the velocity of the passenger with respect

to the ground?

Example: The Bus Ride

6 m/s east 0 m/s

7 m/s east

Question

If you are standing in one place, and your friend walks by you:

a. Are you moving relative to your friend?

b. Is your friend moving relative to you?

c. Are you moving relative to the earth?

d. Is your friend moving relative to the earth?

e. Is either of you moving relative to the sun?

Frame of Reference

No

Yes No

Yes

Both are moving

What is needed to describe motion accurately?

Frame of Reference

Motion

The displacement of an object in relation to objects

considered to be stationary.

What is Motion?

Two kinds of motion:

Linear Motion

Motion in a straight line.

Examples:

1. Driving on a straight road

2. Bowling ball down an alley (No hook)

3. A free falling rock or ball

Two kinds of motion:

Curvilinear Motion

Motion along a curved path.

Examples:

1. Throwing a ball

2. Swinging pendulum

3. Roller Coaster – “The Beast”

4. Spinning lawn-mower blade

Distance

The length of the path between two points.

SI Units

Meter (m)

Kilometers (km)

Distance

Displacement

The direction from the starting point and the length of the

straight line from the starting point to the ending point.

SI Units

Meter (m)

Kilometers (km)

Displacement

Example:

Think about the motion of a roller coaster car.

Describe the distance the coaster moved.

The path along which the car travelled

What would the displacement be for a roller coaster?

Distance from getting on the coaster to getting off the

coaster (Most the time = 0)

Distance/Displacement Example

Formula for displacement

∆d = (d final – d initial )

• ∆d is a Greek letter used to represent the words

“change in”.

• ∆d therefore means “change in d”.

• It is always calculated by final value minus initial

value.

Speed

Speed describes how fast a particle is moving. Speed is a

scalar quantity

Equation

V = d / t

v = speed

d = distance

t = time

Units

km/hr, mi/hr, m/s or ft/s.

Speed

Instantaneous Speed

Speed during a particular instant of time

A car does not always move at the same speed. You can

tell the speed of the car at any instant by looking at the

car’s speedometer.

Instantaneous Speed

In physics, velocity is speed in a given direction.

When we say a car travels at 60 km/h, we are specifying

its speed.

When we say a car moves at 60 km/h to the north, we are

specifying its velocity.

A quantity such as velocity that specifies direction as well as

magnitude is called a vector quantity.

Speed is a scalar quantity.

Velocity is a vector quantity.

Velocity

Constant speed means steady speed. Something with

constant speed doesn’t speed up or slow down.

Constant velocity means both constant speed and constant

direction.

Constant direction is a straight line, so constant velocity

means motion in a straight line at constant speed.

Constant Velocity

If either the speed or the direction (or both) is changing, then the

velocity is changing.

Constant speed and constant velocity are not the same.

A body may move at constant speed along a curved path but it

does not move with constant velocity, because its direction is

changing every instant.

Changing Velocity

The car on the circular track may have a constant speed but not a constant velocity,

because its direction of motion is changing every instant.

Thinker!

The speedometer of a car moving northward reads 60 km/h. It

passes another car that travels southward at 60 km/h. Do both

cars have the same speed? Do they have the same velocity?

Answer:

Both cars have the same speed, but they have different

velocities because they are moving in opposite directions.

Velocity

How is velocity different from speed?

Velocity is speed with direction

V = ∆d / ∆t

Units:

km/hr, mi/hr, m/s or ft/s (with direction)

Velocity can be + or – depending on direction.

If Velocity is constant, motion of the object is uniform.

If Velocity changes, motion of the object is variable.

Velocity Equation

Velocity problems can be solved three ways:

1. Mathematically

2. Graphically

3. Experimentally

Example #1

On a sunny afternoon, a deer walk 1,300 meters east to a creek

for a drink. The deer then walks 500 meters west to the berry

patch for dinner, before running 300 meters west when startled

by a loud raccoon. What is the distance the deer walked and

what is the displacement?

3.1 Assessment

Example #2

On a sunny afternoon, a deer walk 1,300 meters east to a creek

for a drink. The deer then walks 500 meters west to the berry

patch for dinner, before running 300 meters west when startled

by a loud raccoon.

a. What is the deer’s displacement?

b. What is the deer’s average speed if the entire trip took 600

seconds (10 minutes)?

3.1 Assessment

Example #3:

An automobile travels 2,500 m north along a straight road at

constant velocity. The elapsed time is 2 minutes. Calculate the

velocity in m/s.

3.1 Assessment

Example #4:

A jet liner passes over St. Louis at 625 mi/hr, heading straight

towards Kansas City, which is 235 mi away. How much time

elapses (in minutes) before the aircraft passes over Kansas City

if it maintains a constant velocity.

3.1 Assessment

Example #5:

How long will it take the sound of the starting gun to

reach the ears of the sprinters if the starter is stationed at

the finish line for a 100 m race? Assume that sound has a

speed of about 340 m/s.

3.1 Assessment

Example #6:

You drive in a straight line at 10 m/s for 1.1 km, and then

you drive in a straight line at 20 m/s for another 1.0 km.

What is your average speed?

3.1 Assessment