MotionMotionMotionMotionA Study of A Study of

Speed, Speed,

Velocity Velocity

and and

AccelerationAcceleration

A Study of A Study of

Speed, Speed,

Velocity Velocity

and and

AccelerationAcceleration

To describe motion accurately a

FRAME OF REFERENCE is necessary.

A FRAME OF REFERENCE is a system of objects that

are not moving with respect

to one another.

What is Motion?What is Motion?When an object changes position

in relation to a FRAME OF REFERENCE

(an object that is not moving) we say that the object is in motion

For example, a car is in motion when it changes its position with a

FRAME OF REFERENCE such as a tree.

When an object changes position in relation to a FRAME OF

REFERENCE (an object that is not moving) we say that the object is in motion

For example, a car is in motion when it changes its position with a

FRAME OF REFERENCE such as a tree.

When describing motion it is helpful to be able to describe how far an

objected moved and which direction the object moved in.

When describing motion it is helpful to be able to describe how far an

objected moved and which direction the object moved in.

Distance is the length of a path between two

points.

The distance of this car traveled on the track is 50 cm.

Displacement

is the direction from the starting point and the length

of a straight line from the starting point to the ending

point.

Displacement

is the direction from the starting point and the length

of a straight line from the starting point to the ending

point.

Distance and

Displacement are similar

but not the same.

Distance is either zero or

a positive value.

Distance is either zero or

a positive value.

Displacement uses positive and negative numbers.

Positive numbers are for displacement to the right of the origin

&

Negative numbers are for displacement to the left the origin.

Displacement uses positive and negative numbers.

Positive numbers are for displacement to the right of the origin

&

Negative numbers are for displacement to the left the origin.

Distance Vs. DisplacementDistance Vs. DisplacementDistance Vs. DisplacementDistance Vs. Displacement5 km

10 km

11 km

10 km

DistanceDistance: how : how far something far something actually traveled actually traveled total (25km)total (25km)

DisplacementDisplacement: : the length of the the length of the straight line straight line between the between the starting and starting and stopping points stopping points (11km)(11km)

Displacement = ?

Total Distance = ?

Diner from home is 15 km

5 km15 km

25km

15 km

Total Distance = ?

Displacement = 21km

10 km

5 km

Displacement = ?

Total Distance = ?

How many steps did it take to walk around the room?

Where do you end up on his walk?

SpeedSpeedSpeedSpeed

• Speed describes how fast an object Speed describes how fast an object is moving is moving

• If an object is not moving it has no If an object is not moving it has no speedspeed

• Speed describes how fast an object Speed describes how fast an object is moving is moving

• If an object is not moving it has no If an object is not moving it has no speedspeed

Instantaneous speedInstantaneous speed

• A speedometer shows a car’s instantaneous speed.

• The instantaneous speed is the actual speed an object has at any moment.

• A speedometer shows a car’s instantaneous speed.

• The instantaneous speed is the actual speed an object has at any moment.

When an object is covering When an object is covering an equal distance an equal distance

in an equal amount of time, in an equal amount of time, it is moving at a it is moving at a constant speedconstant speed

Most objects do not travel at Most objects do not travel at constant speedconstant speed

• When you divide the total distance of a trip by the time taken you get the average speed.

• On this driving trip around Chicago, the car traveled and average of 100 km/h.

• When you divide the total distance of a trip by the time taken you get the average speed.

• On this driving trip around Chicago, the car traveled and average of 100 km/h.

SpeedSpeedSpeedSpeed

• The speed of a moving object is usually The speed of a moving object is usually different at any given moment, so we different at any given moment, so we must calculate the average speedmust calculate the average speed

• Average Speed (V) = Average Speed (V) = Distance (D)Distance (D) Time (T)Time (T)

Units= m/sUnits= m/s

• The speed of a moving object is usually The speed of a moving object is usually different at any given moment, so we different at any given moment, so we must calculate the average speedmust calculate the average speed

• Average Speed (V) = Average Speed (V) = Distance (D)Distance (D) Time (T)Time (T)

Units= m/sUnits= m/s

D

V T

The units for speed are distance units over time units.

The units for speed are distance units over time units.

We use the term velocity

to mean speed with direction.

We use the term velocity

to mean speed with direction.

Velocity describes the Velocity describes the speed and direction of an objectspeed and direction of an object

• i.e. The car was moving with a velocity of 25m/s easti.e. The car was moving with a velocity of 25m/s east

• Velocity (V) = Velocity (V) = Distance (D)Distance (D) Time (T)Time (T)

Units= m/s + directionUnits= m/s + direction

Velocity describes the Velocity describes the speed and direction of an objectspeed and direction of an object

• i.e. The car was moving with a velocity of 25m/s easti.e. The car was moving with a velocity of 25m/s east

• Velocity (V) = Velocity (V) = Distance (D)Distance (D) Time (T)Time (T)

Units= m/s + directionUnits= m/s + direction

Graphs of MotionGraphs of Motion• Constant speed means the speed stays the

same.

• An object moving at a constant speed always creates a position vs. time graph that is a straight line.

• Constant speed means the speed stays the same.

• An object moving at a constant speed always creates a position vs. time graph that is a straight line.

Speed can be represented in Speed can be represented in a a

Position(distance)-time graphPosition(distance)-time graph

Speed can be represented in Speed can be represented in a a

Position(distance)-time graphPosition(distance)-time graph

TimeTime is the is the independent independent variable variable because because time will time will pass pass whether whether distance is distance is traveled or traveled or notnot

DistanceDistance is is the the dependent dependent variable variable because the because the distance distance traveled traveled depends on depends on how much how much time an time an object is object is movingmoving

• A position vs. time graphs can compare the motion of different objects.

• The steeper line on a graph means a faster speed.

• A position vs. time graphs can compare the motion of different objects.

• The steeper line on a graph means a faster speed.

The steepness of a line is measured by finding its slope.

The steepness of a line is measured by finding its slope.

The slope of a line is the ratio of the “rise” to the “run”.

Most objects do not Most objects do not move at a move at a

constant speedconstant speed

Most objects do not Most objects do not move at a move at a

constant speedconstant speed

Acceleration is the rate at which your speed (or velocity) changes.

Acceleration is the rate at which your speed (or velocity) changes.

If your speed increases by 1 meter per second (m/s) for each second, then your acceleration is 1 m/s per second.

• Acceleration occurs whenever there is a change in speed, direction, or both.

• Acceleration occurs whenever there is a change in speed, direction, or both.

• The word “acceleration” is used for any change in speed, up or down.

Acceleration can be positive or negative.

• The word “acceleration” is used for any change in speed, up or down.

Acceleration can be positive or negative.

• Positive acceleration adds more speed each second.

• Things get faster.

• Speed increases over time.

• Positive acceleration adds more speed each second.

• Things get faster.

• Speed increases over time.

• The position vs. time graph is a curve when there is Positive Acceleration.

• The car covers more distance each second, so the position vs. time graph gets steeper each second.

• The position vs. time graph is a curve when there is Positive Acceleration.

• The car covers more distance each second, so the position vs. time graph gets steeper each second.

• Negative acceleration subtracts some speed each second.

• Things get slower.

• People sometimes use the word deceleration to describe slowing down.

• Negative acceleration subtracts some speed each second.

• Things get slower.

• People sometimes use the word deceleration to describe slowing down.

• When a car is slowing down, the speed decreases so the car covers less distance each second.

• The position vs. time graph gets shallower with time.

• When a car is slowing down, the speed decreases so the car covers less distance each second.

• The position vs. time graph gets shallower with time.

Acceleration describes how quickly speed changes.

Acceleration is the change in speed

divided by the change in time.

Acceleration describes how quickly speed changes.

Acceleration is the change in speed

divided by the change in time.

AccelerationAccelerationAccelerationAcceleration• Acceleration is any change in velocity Acceleration is any change in velocity

(a change in speed and/or direction)(a change in speed and/or direction)

• Acceleration=Acceleration=Final Velocity-Initial Final Velocity-Initial VelocityVelocity

TimeTime• a = a = VVff-V-Vii

tt

Units= m/sUnits= m/s22

• Acceleration is any change in velocity Acceleration is any change in velocity (a change in speed and/or direction)(a change in speed and/or direction)

• Acceleration=Acceleration=Final Velocity-Initial Final Velocity-Initial VelocityVelocity

TimeTime• a = a = VVff-V-Vii

tt

Units= m/sUnits= m/s22

You can be moving (non-zero speed) and have

no acceleration (think cruise control).

You can also be accelerating and not moving!

A falling object begins accelerating the instant it is

released.

You can be moving (non-zero speed) and have

no acceleration (think cruise control).

You can also be accelerating and not moving!

A falling object begins accelerating the instant it is

released.

Free fall Free fall

An object is in free fall

if it is accelerating due to the

force of gravity and no other forces are acting on

it.

An object is in free fall

if it is accelerating due to the

force of gravity and no other forces are acting on

it.

• Falling objects increase their speed by 9.8 m/s every second, or 9.8 m/s2

• Falling objects increase their speed by 9.8 m/s every second, or 9.8 m/s2

The letter “g” is used for acceleration due to gravity.