Distance, Speed and Time
speed (m/s) = distance (m)
time (s)
S=D
T
D
S
x
T
D=SXT
T=D
S
1. An athlete runs 200m in 20s. What is his
speed?
speed = distance
time
speed = 200 m
20 s
speed = 10 m/s
2. A bus travels 2000m between stops at a speed of
40m/s. Find the time taken to travel this distance.
speed = distance
time
40 = 2000
time
time = 2000 = 50s
40
3. It takes a cyclist 30s to go 850 m. What is
her speed?
speed = distance
time
speed = 850 m
30 s
speed = 28.33 m/s
4. A walker travels at 3m/s for a distance of 50m.
How long did it take him?
speed =
distance
time
3 = 50
time
time = 50
3
= 16.67 s
VELOCITY AND SPEED
This car is travelling
at a speed of 20m/s
This car is travelling at a
velocity of 20m/s east
Distance and Displacement
Distance is simply how far something has moved
Man and dog have
walked 3 metres
from X
x
Displacement is ‘distance in a given direction’
Man and dog have
walked 3 metres
WEST from X
x
Acceleration
acceleration (m/s2) = change in velocity (m/s)
time taken (s)
Remember: the formula for acceleration and
deceleration is the same
What does acceleration mean?
The rate at which speed increases
e.g. 5 m/s2
5m/s/s
The speed is increasing by 5m/s every second
0s
1s
5m/s
2s
10m/s
3s
15m/s
4s
20m/s
5s
25m/s
6s
30m/s
Questions on acceleration
1. A cyclist accelerated from rest to 10m/s in 5s.
Find the acceleration.
acceleration = change in velocity
time
=
10 – 0
5
= 2 m/s2
=
10
5
2. A sprinter crosses the finishing line at a speed of
8m/s and comes to rest 10s later. Calculate the
deceleration of the sprinter.
acceleration = change in velocity
time
=
8 – 0 = 8
10
= 0.8 m/s2
10
3. A grand prix car increases its speed from 50m/s
to 120m/s in 3s. What is the acceleration?
acceleration = change in velocity
time
=
120 – 50 = 70
3
= 23.33 m/s2
3
4. A skier increases his speed from 6m/s to 10m/s
in 2s. What is his acceleration?
acceleration = change in velocity
time
= 10 - 6 = 4
2
= 2 m/s2
2
MASS
15 kg
50 kg
Mass is the amount of matter inside an object.
It is measured in kilograms (kg)
GRAVITATIONAL FIELD STRENGTH
On Earth = 10N/kg
g = 10
To find the WEIGHT of of an object you need to know the relationship
between WEIGHT, MASS and GRAVITATIONAL FIELD STRENGTH
weight (N) = mass (kg) x gravitational field strength (N/kg)
= 1 x 10
= 10 N
1kg
g = 10
10 N
Weight is the force of gravity on a body
and is measured in NEWTONS (N). On Earth
the force on a 1kg object is 10N (g = 10N/kg). On the moon
the force on a 1kg object is 1.67N (g = 1.67N/kg)
What is the weight of the Martian if it lands on
the Earth or the Moon?
50kg
To find the weight of the Martian you need to know:weight (N) = mass (kg) x gravitational field strength (N/kg)
W=MXG
M=W
G
W
G=W
M
G
M
Earth (g = 10)
50 kg
weight = mass x g
= 50 x 10
= 500 N
Moon ( g = 1.67)
50 kg
Weight = mass x g
= 50 x 1.67
= 83.5 N
STOPPING DISTANCE OF A VEHICLE
Thinking
distance
Braking
distance
OVERALL STOPPING DISTANCE
Stopping a vehicle
Tiredness
Drugs
Alcohol
Thinking
distance
Wet roads
Icy roads
Tyres/brakes
worn out
Visibility
Braking
distance
Driving too
fast
Stopping a vehicle
brakes
type of
road
surface
alcohol/drugs
Condition of
vehicle
tyres
Condition of
road
wet/icy roads
Condition
of driver
concentration
Distance-Time Graphs
40
30
Distance
(metres)
FASTEST
Constant
Speed
Constant
Speed
20
10
0
Constant
Speed
20
40
At Rest
60
80
100
Time/s
Distance-time graphs (outward/return journey)
40
30
Distance
(metres)
20
10
0
Time/s
20
40
outward journey
60
80
100
return journey
Distance-time graphs (total journey time/total distance travelled)
40
30
Distance
(metres)
20
40m
40m
80m
10
0
20
40
60
100s
80
100 Time/s
Distance-time graphs (finding speed from part of graph)
Distance-time
graphs (finding speed from part of graph)
40
30
Distance
(metres)
20
10
0
20
40
60
80
speed during 1st 20s = distance = 10m = 0.5m/s
time
20s
100 Time/s
Distance-time graphs (average speed for journey)
Distance-time
graphs (average speed for journey)
40
30
Distance
(metres)
20
10
0
20
average speed = 80m
100s
40
60
= 0.8 m/s
80
100 Time/s
DISTANCE / TIME GRAPH
d
i
s
t
a
n
c
e
(m)
500m
D
400m
B
300m
C
200m
100m
E
A
0
10 20 30 40 50 60 70 80 90 100 110 110 120 130 140
Time (s)
Questions on Distance/Time Graph
Find:
1. the average speed during A-B
S = D = 300m = 15m/s
T
20s
2. the average speed between B – C
S = D = 0m
T
=
0m/s
20s
3. the average speed for the return journey
S = D = 460m = 7.67 m/s
T
60s
Speed/Time graphs
Speed (m/s)
4
0
Time (s)
5
This object is travelling at a constant
speed of 4m/s for 5s
Speed/time graphs (acceleration - increasing speed)
s
10
p
e
e
d
(m/s)
0
time (s)
5
This object is increasing speed from
0m/s (rest) to 10m/s in 5s
Speed/time graphs (finding acceleration)
s
10
p
e
e
d
(m/s)
0
time (s)
5
acceleration = change in velocity
time
= 10 – 0
5
=
2 m/s2
speed/time graphs (average speed)
s
p 10
e
e
d
5 m/s
(m/s)
0
time (s)
Average speed = 10 + 0
2
=
5 m/s
5
speed/time graphs (deceleration -decreasing speed)
s
p
e
e
d
20
(m/s)
0
time (s)
This object is decreasing its speed
from 20m/s to 0m/s (rest) in 5s
5
speed/time graphs (finding deceleration)
s
p
e
e
d
20
(m/s)
0
5
time (s)
deceleration = change in velocity
time
= 20 – 0
5
=
4 m/s2
speed/time graphs (average speed)
s
p
e
e
d
20
10 m/s
(m/s)
0
time (s)
Average speed = 20 + 0
2
= 10 m/s
5
Speed/Time graph
VELOCITY (M/S)
constant speed
accelerating
40
30
decelerating
accelerating
20
constant speed
10
0
10
20
30
TIME (S)
40
50
60
What is the acceleration in the 1st 20s?
Acceleration = change in velocity
time
= 30 – 0
20
= 1.5m/s2
What is the deceleration in the last 10s?
deceleration = change in velocity
time
= 40 – 0
10
= 4m/s2
Speed/Time graphs (finding distance travelled)
Speed (m/s)
4
area of the
green rectangle
0
Time (s)
5
distance = area under the graph
distance = speed x time
= height x length
=4x5
= 20m
speed/time graphs (distance travelled)
s
10
p
e
e
d
(m/s)
0
5
time (s)
Area under graph = b x h
2
= 5 x 10
2
= 25 m
speed/time graphs (distance travelled)
s
p
e
e
d
20
(m/s)
0
5
time (s)
Distance travelled = b x h
2
= 5 x 20
2
= 50 m
VELOCITY (M/S)
Speed/Time graph (finding distance travelled)
40
30
20
10
0
10
20
30
TIME (S)
40
50
60
What distance is travelled between 0s & 20s?
40
0
20
Area = b x h
2
= 20 x 40
2
= 800
2
= 400m
What distance is travelled between 20s & 50s?
40
0
Area = b x h
20
50
= 40 x 30
= 1200m
What distance is travelled between 50s & 60s?
40
0
Area = b x h
2
50
60
= 10 x 40
2
= 200m
VELOCITY (M/S)
Speed/Time graph (bigger the area under the graph ………..)
40
30
Bigger the area
under the graph
the further the
distance travelled
20
10
0
10
20
30
TIME (S)
40
50
60
RESULTANT
FORCES
When 2 or more forces act on an object they can be replaced by a single
force called the RESULTANT FORCE
6N
6N
12N
RESULTANT FORCES
4N
4N
0N
RESULTANT FORCES
16N
29N
12N
1N
BALANCED FORCES
OBJECT AT REST (STATIONARY)
3N
3N
RESULTANT FORCE = 3N – 3N = 0N
OBJECT REMAINS AT REST (STATIONARY)
BALANCED FORCES
MOVING OBJECT
3N
3N
RESULTANT FORCE = 3N – 3N = 0N
OBJECT TRAVELS AT CONSTANT SPEED
UNBALANCED FORCES
OBJECT AT REST (STATIONARY)
3N
6N
RESULTANT FORCE = 6N – 3N = 3N
OBJECT INCREASES SPEED FROM REST (ACCELERATES)
UNBALANCED FORCES
MOVING OBJECT
3N
6N
RESULTANT FORCE = 6N – 3N = 3N
OBJECT INCREASES SPEED FROM SPEED ORIGINALLY
MOVING AT
UNBALANCED FORCES
MOVING OBJECT
3N
6N
RESULTANT FORCE = 6N – 3N = 3N
OBJECT SLOWS DOWN FROM SPEED ORIGINALLY
MOVING AT (DECELERATES)
BALANCED FORCES
FALLING OBJECT
AIR FRICTION/RESISTANCE
FALLS AT A CONSTANT SPEED
(TERMINAL VELOCITY)
WEIGHT/GRAVITY
UNBALANCED FORCES
FALLING OBJECT
AIR FRICTION/RESISTANCE
OBJECT INCREASES SPEED
2N
(ACCELERATES)
6N
WEIGHT/GRAVITY
UNBALANCED FORCES
FALLING OBJECT
AIR FRICTION/RESISTANCE
8N
OBJECT DECREASES SPEED
(DECELERATES)
REMEMBER: THE WEIGHT
OF THE OBJECT REMAINS
THE SAME NO MATTER
WHAT SPEED IT FALLS AT
6N
WEIGHT/GRAVITY
AS SPEED
INCREASES
THE
RESISTIVE
FORCES
INCREASE
WEIGHT/
GRAVITY
ALWAYS
STAYS
THE
SAME
UNBALANCED
FORCES
AIR FRICTION/RESISTANCE
20m/s
2N
6N
30m/s
5N
6N
WEIGHT/GRAVITY
ACTION/REACTION FORCES
For every ACTION force
there is an EQUAL but
OPPOSITE REACTION force
Wall pushing
man
Man
pushing
wall
RECOIL
BULLET
REACTION
FORCE
ACTION
FORCE
What 2 things affect the acceleration of this car?
• MASS measured in kilograms
• RESULTANT FORCE, the difference between the
force due to friction and the force of the engine
Resultant Force, Mass and
Acceleration
resultant force (N) = mass (kg) x acceleration (m/s2)
f= mxa
F
a=f
m
M
A
m=f
a
motion
10N
5kg
10N
f=mxa
0=5xa
a = 0 = 0m/s2 = constant speed
5
motion
15N
3kg
f=mxa
5=3xa
a = 5 = 1.67 m/s2
3
20N
55m/s2
300N
f = m x a
300 = m x 55
m = 300 = 5.45 kg
55
ACCELERATION DUE TO GRAVITY
If an elephant and a feather
were dropped from the
same height, which one
would hit the ground first?
Due to air
resistance on
the feather and
the elephants
greater mass
the elephant
would hit the
ground first
If we ignore air resistance
the elephant and feather
would land on the ground at
the same time due to their
ACCELERATION DUE TO
GRAVITY being the same!!!
All objects will accelerate
downwards at the same rate
if air friction is ignored so
they will hit the ground at the
same time!
The acceleration g = 10m/s2