### Motion

```Physical Science
Chapter 11 – Part 1
Non-accelerated Motion
Chapter 11.1-11.2
Frame of Reference
• A system of objects that are not moving with
respect to one another
• A reference point or system
• BASICALLY …. Something unchanging to
measure things from
• Good frames of reference for measuring the
motion of a car…
• The Earth, the road, buildings, trees
• Bad frames of reference for measuring the
motion of a car….
• Clouds, other cars on the road, bikers, flying birds
Relative Motion
• Movement in relation to a frame of reference
• All Motion is Relative
• This means… all motion is based on someone’s or something’s
perspective
• Examples
• School busses
• Cars on highway
• LabQuest
Relative Motion
Or a more
recent example
Measuring Distance
• Length of a path between two points
• When an object moves in a straight line, the distance is the length
of a line connecting the starting point and the ending point
• SI Unit – meters
• Other options- km, mi, cm
Displacement
• Distance with a direction
• Distance – 5 kilometers
• Displacement – 5 Kilometers North
• How much an object is displaced
• When objects travel in a straight line the magnitude (amount) of
the displacement is equal to the distance travelled
• When an object does not travel in a straight line, distance and
displacement will be different
Vectors
• Vector Quantities
• Have magnitude and direction
• Scalar Quantities
• Only have magnitude
• Vector quantities can be represented with arrows of a scaled
length
• Length shows magnitude
• Arrow shows direction
3 km
3 km
3 km + 3 km = 6 km
Vectors & Scalars
VectorsHave Magnitude & Direction
ScalarsHave only Magnitude
Examples
Examples
Displacement
Distance
Velocity
Speed
Acceleration
Mass
Force
Time
Displacement in a straight line
4 km
7 km
4 km + 7 km = 11 km
8 km
5 km
8 km - 5 km = 3 km
Displacement that isn’t on a straight Path
3 km
• Resultant Vector
(red) – vector sum
of 2 or more
vectors
1 km
2 km
1 km
1+1+2+3 = 7 km
Finding Displacement using Vector
• These two vectors have the same ________________ and
opposite ________________.
• These two vectors have different ________________ but
the same ________________.
• These two vectors have the same ________________ AND
the same ________________.
average Speed
• Average Speed is equal to distance divided by time
• =

• How fast or slow something is going
• A rate of motion
Instantaneous Speed
• Speed at a given moment of time
• What the speedometer on a car reads
Constant Speed
• When speed is not changing
• Instantaneous speed is equal to average speed at all
times
• NOT Speeding up or slowing down
• Only ways to change speed is to speed up or slow down
Average Speed
Constant Speed Instantaneous Speed
The Average speed over
some time
Maintaining the same Speed of an object at a
speed all the time
particular moment in time
Velocity
• Speed AND direction that an object is moving
• Vector Quantity
• + means North, Up, East, or to the Right
• - means South, Down, West, or to the left
• Sometimes multiple velocities can affect an objects motion
• Sailboat, airplanes
• These velocities combine with Vector Addition
Speed vs. Velocity
• Speed – tells how fast something is moving
• Ex. 100 km/hr
• Velocity – tells how fast something is moving and its direction
• Ex. 35 mph North
• Can an object move with constant speed but have a changing
velocity?
• Can an object move with constant velocity but have a changing
speed?
2 ways to change Speed
Speed Up
Slow Down
3 ways to change Velocity
Speed Up
Slow Down
Change Direction
acceleration
• Acceleration – The rate at which velocity changes
• Can be described as ….
• Changes in Speed
• Changes in Direction
• OR change in both Speed and Direction
• Vector Quantity
• Units are meters per second per second or m/s2
3 Way to Accelerate
Speed Up
Slow Down
Change Direction
Can an object moving with constant speed be accelerating?
Devices in Cars that lead to acceleration
Calculating Acceleration
ℎ

∆

−
• =
= =

•Divide the change in velocity by total
time
Example
• A car starts from rest and increases its speed to 25 m/s over the
course of 10 seconds. What is the car’s acceleration?
•=
•=
−

(25
=
−
10

0)

0

=
m
2.5 2

=

25

= 10
=
−

=

(32

=

=

− 10 )
= 7.33 m
3
2
=
Graphs of motion
• Motion can also be depicted very well using graphs
• Two types of graphs
Displacement (m)
• Displacement vs. time (D-t) graphs
• Velocity vs. time (V-t) graphs
Straight,upward
line on D-t graph
means constant
velocity
Straight,upward
line on a V-t
graph means
constant
acceleration
D-t graph of constant ‘v’
• Displacement increases at regular intervals, so constant
velocity
▫ Graph below Increases displacement by 5 meters every sec.
• To find vel. on a disp.- time graph, find Slope
30
(
d
25
i
s
20
p
l t 15
a
c m10
e
m
5
e
0
n
)
0
1
2
3
time (s)
4
5
6
Slope
• Tells the rate of increase of the y-value as you move across the x values for any graph
• Slope = rise / run
• In other words… how much the graph goes up divided by how much the graph goes across
• Slope tells us properties of the motion being depicted
• On a displacement time graph  slope = velocity
• On a velocity-time graph
 slope = acceleration
30
Rise/run=slope= 25/5 =
5 m/s
(
d
i
25
s
p
20
l
15
a
m
c
10
e
m
5
e
n
0
t
)
Rise = 25
0
1
time (s)
2
3
Run = 5
4
5
6
If you took slope of
smaller sections of the
graph you would get
‘v’ is constant
The slope of ______________ lines indicates ______________.
When tangent lines become ______________ with time, this means that the object is
______________ up. (It was originally at ______________.)
The object is moving ______________ from the reference point with time.
The tangent lines are getting ______________ steep with time.
This means that the object is ______________ down (to a ______________).
Because distance is ______________ with time, the object is moving ______________
from the reference point.
Velocity- Time graphs
• v v. t graphs may look the same as
some D v. t graphs, but the motion
they describe can be very different
because they deal with velocity,
not distance.
• **The slope, of a Velocity v. Time
graph indicates Acceleration**.
The object has ______________ acceleration.
The object moves with _________________ velocity.
What motion does this graph represent?
This object is at ______________ because its velocity is always
______________.
This object’s velocity is _________________ with time.
This graph shows ________________ acceleration (one _____________).
This object is _________________ up.
Distance-time graph of changing velocity
30
25
d
i
20
s
t
a 15
n
c
e 10
Displacement
(m)
0
0
1
8
2
11
3
18
4
15
5
25
(
Time
(s)
m
)
5
0
0
1
2
3
Time (S)
What is v for 0-1 sec.??
What is v for 0-2 sec.??
What is v for 3-5 sec.??
What is v for 0-5 sec. ??
4
5
6
Distance-time graph of constant
acceleration
• Parabola….. If + acc, line keeps getting steeper and steeper
d
t
30
V 25
e
l
o 20
c
i
15
t
y
5
)
(
10
m
/
s
0
0
1
2
3
4
5
6
Time (S)
• Avg. velocity from 0-1 sec. ? 4 m/s
• Avg. vel. From 3-4 sec? 16.5
• Acc. From 2-3 sec? 7 m/s2
Velocity vs. Time graph of constant acceleration
Velocity
(m/s)
• Speed-time graph
• Slope = rise/run …
• Rise =
▫
16
• Run =
▫
4
• Rise/run =
▫
4 m/s = acceleration
• Position –time Graph
• Slope = rise/run …
• Rise =
▫ 50
• Run =
▫ 5
• Rise/run =
▫ 10 m/s = speed
Free Fall Acceleration
• As objects fall toward the Earth they are accelerating at
a rate of 9.8 m/s2 downward
2
2
• We can usually round 9.8 m/s to 10 m/s
• Objects in free fall will gain 10 m/s of speed for every 1
second it is falling
Time (sec)
Instantaneou Acceleration
s Speed (m/s) (m/s2)
0
0
10
1
10
10
2
20
10
3
30
10
4
40
10
Free Fall Acceleration
• Object is in free-fall any time it is ONLY under the
influence of gravity
• Including when something is thrown upwards
• All objects (regardless of mass) fall at the same rate
on Earth, when air resistance is ignored
Time (sec)
Instantaneou
s Vel. (m/s)
Acceleration
(m/s2)
0
+30
-10
1
+20
-10
2
+10
-10
3
0
-10
4
-10
-10
5
-20
-10
6
-30
-10
Ball thrown
upward with
initial
velocity of
+30 m/s
```