Motion
Speed, Velocity,
and Acceleration
What is motion?

Motion is easy to recognize but can be hard to
describe

Motion simply put is a change in position

The following quantities are used to describe
motion: speed, velocity and acceleration

Each of these is a rate. A rate is a quantity
divided by time.
Recap: Motion

Motion
Change in position during a
time period
 3 types of motion

Speed
 Velocity
 Acceleration

So how is a difference in position
determined?

First let us define distance

It is simply the linear space between two points
 So
from where do we begin our
measurement?
From
a point of reference
Point of Reference

Movement is relative to an object that appears to be stationary

This means that we describe motion of an object relative to
some other object

The object or point from which movement is determined is
called the point of reference

For us, the reference for motion is Earth or Earth’s
surface, and speed and distance are measured relative to
the earth
In Which Direction Does Motion
Occur?

Motion can occur in many directions; this can be
exhibited on a coordinate axis

We generally determine distance along the x-axis,
and for our calculations we will use the x-axis
 But
there are 2 other axes on which motion occurs (we
will address this later)
Now that we have determined
direction, how do we decide what
factors we will consider?

Sometimes when we make calculations we are
not concerned with the direction; while other
times direction becomes a very important factor
that must be accounted for.

Because of this, dimensional (measurable) quantities
have been separated into 2 categories…
 Scalar
Quantities
 Vector Quantities
Characteristics of a Scalar
Quantity
Only has magnitude (greatness of a measurement)
 Requires 2 things:
1. A value (a number)
2. Appropriate units
Ex. Mass: 5kg
Temp: 21° C
Speed: 65 mph

Characteristics of a Vector Quantity
Has magnitude & direction
 Requires 3 things:
1. A value
2. Appropriate units
3. A direction!
Ex. Acceleration: 9.81 m/s2 down
Velocity:
25 mph West

Vector Quantities

The best way to remember this is that a vector
must have magnitude and direction….
Oh Yeah!
Speed
Question
 When
can you determine
how fast you are going in
a jet plane?
Speed

Speed
1. Definition: Rate at which
an object moves
 2. Formula: Distance divided
by time (d/t)
 3. Units: m/s or km/s

Speed
Speed is a measure of how fast something is
moving.
 It is the rate at which a distance is covered
 Units of speed could be: km/h, m/s, mi/h, ft/s
 In physics we use units of m/s for speed
 Speed is a scalar quantity

speed


distance
time
d
s
s = d/t
t
Instantaneous Speed
Instantaneous speed is speed at any instant in
time.
 A speedometer measures speed in ‘real time’
(the instantaneous speed).

Average Speed


Average speed is the average of all
instantaneous speeds; found simply by a total
distance/total time ratio
The average speed of a trip:
average speed 
total distance
elapsed time
Average speed
 Total
distance divided by the
total time
 Formula:
 Total distance

total time
Calculating Speed: Example

If 2 runners ran the same distance (10km)
but one completed it in 3600 seconds and
the other in 2800 seconds, what were
each of their average speeds?

1: d/t
10.0 km/3600. sec
0 .00278 km/sec

2: d/t
10.0 km/ 2800. sec
0 .00357 km/sec

Runner 2 has greatest average speed!
Calculating Speed:
Example

Spirit of Australia, a hydroplane boat, made
speed records by traveling 239 miles in 0.75
hours (45 minutes). What is it’s record
breaking speed?

d/t 239 miles/ 0.75 hr
318.7 mph
or ~320 mph
Velocity
Velocity
 Speed
in a given direction
 Velocities in the same
direction combine by adding
 Velocities in different
directions combine by
subtracting
Velocity Triangle
Speed and velocity triangles are similar because v
= d/t
 Find the equation for displacement, and time
using the triangle
 d=vxt
 t = d/v
d

v
t
Velocity

Velocity
1. Definition: Rate at which
an object moves in a given
direction
 2. Formula: Displacement
divided by time (d/t)
 3. Units: m/s, km/s.km/hr,
mph


And direction: North, South, East or
West
Calculating Velocity:
Example
 If
a runner is running east at 10 m/s
sec, what is her velocity?
 10
m/s east
Calculating Velocity:
Example

If you’re rowing a boat downstream at 16
km/hr, and the current is moving at 10.0
km/hr. How fast does the boat “look” like
it’s going to someone on shore? (Draw a
picture too!)

16 km/hr + 10.0 km/hr

26 km/hr downstream
Calculating Velocity:
Example
 If
you’re rowing a boat upstream at
15 km/hr, against a current moving at
8 km/hr. What is you’re actual
velocity to an observer on the shore?
 15

km/hr - 8 km/hr
7 km/hr upstream
Calculating Velocity:
Example


If you are running up an escalator at 2 steps
per second and its moving downward at 3
steps per second, what is the total velocity?
In what way are you moving?
-3 steps/s + 2 steps/s
 -1 step/s

(you are actually moving backwards, down the
escalator, although you’re running up it)
Velocity Questions
1)
2)
3)
4)
How far does Bob run if he maintains an average
velocity of 3 m/s for 10 s?
30 m
List three ways you can change the velocity of your
car. Speed up, Slow down, turn
Is it possible to go around a corner without changing
velocity? Explain.
NO
One car is going 25 miles/hr north, another car is
going 25 miles/hr south. Do they have the same
velocity? Explain. They do not have the same velocity
because they are travelling in
different directions!
Velocity

Velocity

Velocities can be combined
Add velocities when in same
direction
 Velocities in opposite direction=
subtract

More about Vectors
We represent a vector by drawing an arrow

1. the length represents magnitude

2. the arrow faces the direction of motion
 When we add or subtract vectors the result is
called the resultant

Mathematical Addition of Vectors

Vectors in the same direction:
Add the 2 magnitudes, keep the direction
the same.
Ex.
+
=
3m E
1m E
4m E
Mathematical Addition of Vectors

Vectors in opposite directions
Subtract the 2 magnitudes, direction is the
same as the greater vector.
Ex.
4m S +
2m N =
2m S
Mathematical Addition of Vectors

When vectors meet at 90°
The resultant vector will be hypotenuse of a right
triangle.
 Use the Pythagorean Theorem to find the resultant.

a2 + b2 = c2
Vectors at a right angle

Determine your resultant velocity if you are
traveling in a boat 40 km/hr North and the
river’s current is moving 30 km/hr East.
a2 + b2 = c2
 (40 km/hr)2 + (30 km/hr)2 = c2
 1600 km2/hr2 + 900 km2/hr2 = c2
30 km/hr
 2500 km2/hr2 = c2
40 km/hr
 √ 2500 km2/hr2 = √ c2
 C= 50 km/hr

Questions
 How
is velocity different
from speed?
 Which two factors
determine an object’s
velocity?
Velocity and Speed

In physics we distinguish between speed and velocity:

Speed refers to how quickly an object moves (a scalar quantity).

Velocity is defined as speed in a given direction or rate of
change of position (displacement over time). v = x/t

Velocity refers to both the speed and direction of motion of
an object (a vector quantity).

Negative velocity means the object is moving in the opposite
direction

Motion at constant velocity means that both the speed and
direction of an object do not change.

In a car, we can change the velocity three ways: gas pedal to
speed up, brake to slow down or steering wheel to change
direction
Acceleration

Acceleration

1. Definition: Rate of change
in velocity

Speeding up, slowing down,
changing direction
2. Formula: Final velocity
minus original velocity,
divided by time
 3. Units: m/s/s or km/s/s


Acceleration
4. Increasing velocity positive acceleration
 5. Decreasing velocity negative accelerationdeceleration

Acceleration
 The
change in velocity
 Acceleration is measured in
m/sec/sec or m/sec2
 Formula is:
 (final
velocity – initial velocity)
time
Acceleration

For its velocity to change, an object must
accelerate.

An object accelerates whenever its speed or
direction or both change.

Acceleration may be positive (increasing speed)
or negative (decreasing speed).

Acceleration is a measure of how quickly the
velocity changes: a = Dv/t
accelerati on 
change of velocity
time interval
Acceleration at constant speed

An object moving in a circle at constant
speed is always accelerating (changing
direction).
Solving Acceleration Problems using
Acceleration Triangle



If you have starting and ending velocity or speed, find
that before you use the triangle.
If not, use triangle to find change in velocity (Dv), then
find initial or final velocity
Dv = final velocity – initial velocity
Dv
a
t
Deceleration vs. Acceleration
A
decrease in velocity is
deceleration or negative
acceleration
 An
increase in velocity is
a positive acceleration
Change in Velocity



Each time you take a step you
are changing the velocity of
your body.
You are probably most familiar
with the velocity changes of a
moving bus or car.
The rate at which velocity
(speed or direction) changes
occur is called acceleration.
Acceleration= final velocity- initial velocity
time
Change in velocity = final
velocity
–
Acceleration= change in velocity
time
initial
velocity
A car traveling at 60. mph accelerates to
90. mph in 3.0 seconds. What is the
car’s acceleration?
Acceleration
=
Velocity(final) - Velocity(initial)
time
=
=
90. mph – 60. mph
0.00083 hours
30 mph
0.00083 hours
= 36000 mph2
A car traveling at 60.0 mph slams on the breaks to
avoid hitting a deer. The car comes to a safe stop
6.0 seconds after applying the breaks. What is the
car’s acceleration?
Acceleration =
V f - Vi
time
=
=
0.0 mph – 60.0 mph
0.00167 hours
- 60.0 mph
0.00167 hours
= - 36000 mph2
Calculating Acceleration:
Example


A roller coaster’s velocity at the top of a
hill is 10m/s. Two sec later it reaches the
bottom of the hill with a velocity of 26 m/s.
What is the acceleration of the roller
coaster?
vf-vi
t
26 m/s -10 m/s
2s
8 m/s*s or 8 m/s2
Calculating Acceleration:
Example

A roller coaster’s velocity at the bottom
of a hill is 25 m/s. Two seconds later it
reaches the top of the next hill, moving
at 10.0 m/s. What is the deceleration of
the roller coaster?

a=
vf-vi
t
a = 10.0 m/s-25 m/s = -7.5 m/s2
2.0 s
Calculating Acceleration:
Example

A car is traveling at 60.0 km/hr. It
accelerates to 85 km/hr in 5.0 seconds.
What is the acceleration of the car?

a = vf-vi
t
a = 85 m/s-60.0 m/s = 5.0 m/s2
5.0 s
Free fall







The constant acceleration of an
object moving only under the
force of gravity is "g".
The acceleration caused by
gravity is 9.81 m/s2
If there was no air, all objects
would fall at the same speed
Doesn’t depend on mass
After 1 second falling at 9.81 m/s
After 2 seconds 19.62 m/s
3 seconds 29.43 m/s
Free fall, an example of
acceleration

Free fall is when an object is falling being
affected only by gravity. That means NO air
resistance.
Free Fall – All objects fall at the same
rate

If you drop a coin and a feather at the
same time you will notice that the coin
reaches the ground way before the
feather.

However, if you were to take the air
out of the container you would find
that the coin and feather fall together
and hit the bottom at the same time!
Acceleration due to gravity, g



Newton told us that every object with mass attracts every other
object with mass and the size of the attraction depends on the
mass of each object and the distance between the objects
We don’t feel the attraction of most objects because their mass
is small relative to the Earth which has a huge mass.
The Earth pulls so that objects experience an acceleration of
about 10 m/s2. This acceleration is given a special letter, g.

g = 9.81 m/s2 This number is important, remember it!

So during each second an object is in free fall, its velocity
increases by 9.81 m/s. If the object experiences air resistance its
velocity won’t increase as fast because air resistance will slow it
down.
Falling
Air resistance will
increase as it falls faster
 An upward force on the
object
 Eventually gravity will
balance with air
resistance
 Reaches terminal velocity
- highest speed reached
by a falling object.

Challenge Question

Suppose someone throws a ball straight
upward with a speed of 30 m/s and at
the same time throws one straight
down with a speed of 30 m/s. Which
ball will be traveling faster when it hits
the ground, the one thrown straight
upward or the one thrown straight
down? Assume there is no air
resistance.