Motion
What is the motion?
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Motion is the area of physics that
studies how things move. It was
developed about 300 years ago
by Isaac Newton. He discovered
that all objects move according to
three basic laws.
In physics, motion is the
phenomenon in which an object
changes its position over time.
Motion is mathematically
described in terms of
displacement, distance, velocity,
acceleration, speed, and time.
Velocity, Acceleration, Speed
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Speed is the rate of motion, or the rate of change of position. It is
expressed as distance moved (d) per unit of time(t). Speed is a scalar
quantity with dimensions distance/time. Speed is measured in the same
physical units of measurement as velocity, but does not contain an
element of direction.
Acceleration, (symbol: a) is defined as the rate of change of velocity. It is
thus a vector quantity with dimension length/time². In SI units,
acceleration is measured in meters/second².
Average speed is distance divided by time.
Velocity is speed in a given direction. Acceleration is
change in velocity divided by time.
Motion Graphs
1.
Speed
Speed .
Distance ( m or cm )
( m or cm/second ) 
.
Time
( seconds )
D
S
T
Nb VELOCITY (v)is simply speed in a given direction
DISPLACEMENT (S) is the distance in a given direction
Examples using the Speed Formula (Showing full working):
1. The sprinter ran 100 metres in 10 seconds. What was his speed ?
Speed
Distance
100 m


Time
10 s
 10 m / s
2. The porsche travelled at 40 m/s for 2 minutes. How far did it go ?
Distance  Speed  Time  40 m / s 120 s  4800m
2. Acceleration
The acceleration of something tells us how quickly its speed is changing.
We can say that acceleration is the amount ………..changes
speed
per …….…...
second
Change in Speed ( metres/second )
2
Acceleration ( metres/second ) 
Time ( seconds )
or
Change in Speed
Acceleration 
Time
v u

t
S
A
T
Where v = final velocity
u = initial velocity
1. The ferrari was travelling at 20 m/s behind a lorry. It pulled out to
overtake and accelerated at 4 m/s2 for 2 seconds. What was its new
speed ?
Change in speed  Acceleration  Time
 4 m / s2  2 s
New Speed = Old Speed + Change in Speed
= 20 m/s + 8 m/s = 28 m/s
 8m / s
4. Motion Represented on Graphs.
There are two types of motion graphs, and three
types of motion. Best represented in a table.
Distance/Time
Stopped
V
150
t
Const’
Velocity
Velocity Time Graph for parachutist.
Velocity/Time
D
Question
V (m/s)
t
15
D
V
T (s)
15
50
100
A. What was his acceleration from 0 to 15 sec ?
t
Const’
Accel’n
t
D
V
A
V
T

150 m / s
15 s
 10m / s 2
B. What was happening at 50 seconds?
He had just opened his parachute and was
decelerating.
t
Gradient = Velocity
t
C. Approximately how far did he fall altogether?
Gradient = Accel’n
Area = Distance
Area under graph  50  150 + 50  15 = 8250m
travelled
Distance time graphs ;Summary
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The gradient of a distance time
graph gives the velocity
increasing gradient means object
is accelerating
decreasing gradient means object
is decelerating
zero gradient means object is
stationary
Velocity time graphs; Summary
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The gradient of a velocity time graph gives the
acceleration of an object
the area under a velocity time graph gives the total
distance traveled
Increasing or decreasing gradient gives the rate at
which the acceleration is increasing or decreasing
Zero gradient means the object is travelling at
constant speed
Problems
1. Calculate the speed over OA AB and BC
5, 0, 3.75m
2. Calculate (a)the acceleration over OA, AB and BC
(b) the total distance traveled in the 12 s
5m/s2, 0, 3.75m/s2, 127.5m
Motion graphs
It is often easier to show the motion of an object with a graph
rather than with words.
There are 2 types of graph we will look at:
 Displacement– time graphs (or distance – time graphs.)
 Velocity - time graphs (or speed- time graphs.)
12
•
•
•
•
With both types of graph, time is plotted on
the x
axis.
The further to the right along the x axis we go – the
longer the time from the start!
Velocity, distance etc are always plotted on the
y axis.
We assume the initial direction of motion to
be
positive.
13
0
1
2 3
Distance (m)
4 5 6 7
8
9 10 11
A body at rest. Ie it is stopped
or standing still!
0
1
2
3
4
5
6
7
8
9
10 11 12
time (s)
14
0
1
2 3
Distance (m)
4 5 6 7
8
9 10 11
An object moving at constant speed.
Constant speed because the lines are straight!
Which line shows the object going fastest?
0
1
2
3
4
5
6
7
8
9
10 11 12
time (s)
15
8
7
6
5
4
2 3
1
0
Distance (m)
9 10 11
Speed is given in m/s so we can work
out the speed here by saying
speed = rise/run = distance/time.
Work it out for each.
0
1
2
3
4
5
6
7
8
9
10 11 12
time (s)
16
0
1
2 3
Distance (m)
4 5 6 7
8
9 10 11
A body accelerating!
You can see that the speed is increasing: the distance
travelled is more each second so this shows it is
accelerating!!
0
1
2
3
4
5
6
7
8
9
10 11 12
time (s)
17
Lets look at an example:
First we will give the information in words then as a
displacement – time graph.
Mark starts from point A and travels at 2m/s for 3 seconds to
point B. He then stops at point B for 4 seconds before going
back towards point A at an initial velocity of -1.5m/s for 2
seconds then stopping at an intersection for 1 second
before continuing to point A at -1.5 m/s.
Ok – lets look at this graphically!!!!!
18
1
2 3
4
5
6
7
8
Much Easier
than words!!!
0
Distance (m)
9 10 11
Marks’ trip
0
1
2
3
4
5
6
7
8
9
10 11 12
time (s)
19
2 3
4
5
6
7
8
9 10 11
What is the difference between this
graph and the ones we looked at
before??
1
0
Speed (m/s)
This axis
has
SPEED
not
distance
on it!!!!
0
1
2
3
4
5
6
7
8
9
10 11 12
time (s)
20
2 3
4
5
6
7
8
It shows that the object is
moving at a constant
speed of 5.5m/s
1
0
Speed (m/s)
9 10 11
So what does this graph show?
0
1
2
3
4
5
6
7
8
9
10 11 12
time (s)
21
What does this graph show?
8
7
6
5
4
2 3
1
0
Speed (m/s)
9 10 11
It shows that the objects’
speed is increasing or the
object is accelerating!
0
1
2
3
4
5
6
7
8
9
10 11 12
time (s)
22
1
2 3
4
5
6
7
8
It shows that the objects’
speed is decreasing or
the object is decelerating!
0
Speed (m/s)
9 10 11
What does this graph show?
0
1
2
3
4
5
6
7
8
9
10 11 12
time (s)
23
Which line shows faster acceleration? Green or blue?
8
7
6
5
4
2 3
1
0
Speed (m/s)
9 10 11
Acceleration = speed/time so
Blue = 3m/s/s
Green = 1m/s/s
Steeper slope = faster
acceleration!
0
1
2
3
4
5
6
7
8
9
10 11 12
time (s)
24
8
Steady
speed
4
5
6
7
Fast
acc
n
Fast
deceleration
Or
negative
acceleration
2 3
Slow
accn
1
0
Speed (m/s)
9 10 11
Putting it all together:
0
1
2
3
4
5
6
7
8
9
10 11 12
time (s)
25
1 2 3 4 5 6 7 8 9
Time (s)
Gradient = rise/run
= 30/6
= 5m/s
= speed!
1 2 3 4 5 6 7 8
Speed (m/s)
10 20 30 40 50 60
Distance (m)
What other information can we get from displacement – time
and speed time graphs?
1 2 3 4 5 6 7 8 9
Time (s)
Gradient = rise/run = 7/7 = 1m/s/s = acceleration!!!
Area under the graph = ½ time x speed
= s x m/s
=m
= distance travelled!!!
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Lets look at the last example and work out
the distance travelled.
27
8
7
6
5
4
2 3
1
0
Speed (m/s)
9 10 11
Work out the area under the line to
work out the distance travelled
0
1
2
3
4
5
6
7
8
9
10 11 12
time (s)
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