Distance, Speed, time, Acceleration introduction

2. Licensed for use in your school only (© 2009)
Something is in motion
if its position is
changing.
There are four
quantities related to
motion:
• distance
• speed
• time
• acceleration
Defining motion
2SCIENCE 1.4: MOTION

3. Licensed for use in your school only (© 2009)
Answer:
123,000 m
Distance refers to how far
an object travelled.
It is usually measured in:
• Metres (m)
• Kilometres (km)
• Centimetres (cm)
Distance (d)
3SCIENCE 1.4: MOTION
1km = 1000m
1m = 100cm
How many metres is it from
Porirua to Palmerston North?

4. Licensed for use in your school only (© 2009)
Time refers to how long a
journey or activity takes.
It is usually measured in:
• seconds (s)
• minutes (min)
• hours (hr)
Time (t)
4SCIENCE 1.4: MOTION
Answer:
2.7 hours
1 hour = 60 minutes
1 minute = 60 seconds
How many hours
is 162 minutes?

5. Licensed for use in your school only (© 2009)
Speed refers to how fast
an object travelled or
how fast it is travelling.
It can be measured in
two ways:
• Average speed
• Instantaneous speed
Speed / velocity (v)
What units is speed
measured in?
The units for speed are:
5SCIENCE 1.4: MOTION
km/hr km.hr-1
or
m/s ms-1

6. Humans reach terminal velocity of 180-230 kmh-1 after
10-12 seconds of free-fall.
In sky-diving, experienced jumpers can reach speeds
of over 200 kmh-1 by falling head-first in a straight-
bodied position (which limits air resistance).
The fastest bird is
the peregrine
falcon which can
reach speeds of
324 kmh-1 when
diving to catch
and kill its prey.
Its amazing
swooping speed
makes it the
fastest creature
on earth.
The fastest fish is the sailfish which has been clocked
leaping out of the water at speeds of 110 kmh-1.
The fastest land
animal is the
cheetah which
can maintain
speeds of 100
kmh-1 for up to
550m.
What do you think is the fastest:
• land animal?
• fish?
• bird?
Estimate the maximum speed that each is
able to reach.
In what popular adventure activity do
humans reach their terminal velocity?
What speed can they reach?

7. Licensed for use in your school only (© 2009)
The average speed for a
journey, or part of a
journey, is calculated by
dividing the distance
travelled by the time
taken.
Average speed (vav)
v
d
t
7SCIENCE 1.4: MOTION
Average speed =
distance
time
vav
=
d
t
t =
d
v
d = v x t
Write the equations to
calculate distance (given
speed and time) and time
(given speed and distance).

8. Licensed for use in your school only (© 2009)
Magic triangles can
help us rearrange
equations.
Simply cover the
quantity you need to
calculate and it will
show you the correct
form of the equation.
Special skill – Using a magic triangle
v
d
t
In the exam you will be given two
quantities and need to find the third.
E.g. Tim ran 400m at an average
speed of 5ms-1. How long did it
take him to complete the race?
The quantity that you need to calculate
is time (t) therefore cover up the t and
write out the equation.
Insert values
Rearrange
equation
= 80 seconds Solve
8SCIENCE 1.4: MOTION
t =
d
v
=
400m
5ms-1

9. Licensed for use in your school only (© 2009)
Instantaneous speed is the
actual speed at any one
moment.
When travelling in your car,
the speed of the vehicle
will usually vary
considerably across time.
If the speed does not
change it is said to be
uniform or constant.
Instantaneous speed
The speedometer in a car
measures the instantaneous
speed of the vehicle.
9SCIENCE 1.4: MOTION

10. Licensed for use in your school only (© 2009)
Answer: the object has stopped / is stationary
Distance – time graphs
show the time taken to
travel a certain distance.
Changes in the slope of the
graph show changes in the
speed of the object.
Distance (d) is plotted on
the vertical axis and time (t)
is plotted on the horizontal
axis.
Distance – time graphs
Time
Distance
What would a horizontal line on the graph represent?
10SCIENCE 1.4: MOTION

11. Licensed for use in your school only (© 2009)
Stationary object
Time
Distance
Constant speed
Time
Distance
Distance – time graphs
Vehicle 1
Vehicle 2
11SCIENCE 1.4: MOTION
Answer: Vehicle 1 is moving more quickly.
Which vehicle in graph two is moving more quickly?
Graph one Graph two

12. Licensed for use in your school only (© 2009)
On a distance-time graph,
the slope of the graph
represents the speed of
the object.
To work out the slope
(gradient) of the graph,
we use the following
equation:
Using graphs to calculate speed
Time
Distance
y-axis
x-axis
Rise
Run
12SCIENCE 1.4: MOTION
slope =
Rise
=
Change in y-axis
Run Change in x-axis

13. Licensed for use in your school only (© 2009)
Question:
A
B
Calculate the speed of the object between A and B
Rise = 40 - 10
Run = 6 - 2
13SCIENCE 1.4: MOTION
Time (s)
speed =
40-10
=
30
= 7.5ms-1
6-2 4

14. Licensed for use in your school only (© 2009)
Accelerating object
Time
Distance
Decelerating object
Time
Distance
Curved distance – time graphs
Deceleration is also referred to as ‘negative acceleration’.
14SCIENCE 1.4: MOTION

15. Licensed for use in your school only (© 2009)
Question:
A
B
C
D
15SCIENCE 1.4: MOTION
D) Susan has stopped
walking for 4 seconds.
C) Susan slows down slightly,
walking 10m in 4s, at a
constant speed of 2.5m/s.
B) Susan picks up the pace,
running this 30m section of
her journey at a constant
speed of 7.5m/s.
A) Susan starts her journey at
a brisk walking pace, covering
her first 20m in 4s, at a
constant speed of 5m/s.
Explain what is happening
at each stage of the graph.
Quote values in your
answer.

16. Licensed for use in your school only (© 2009)
In common speech, the term
acceleration describes only
increasing speed; decreasing
speed is called deceleration.
But in physics, we refer to
any change in speed as
acceleration and measure it
in meters per second per
second (ms-2).
Acceleration (a)
▲ represents ‘change in’’
a
▲v
16SCIENCE 1.4: MOTION
Acceleration =
change in speed
change in time
a =
▲v
▲t
▲t

17. In 10 seconds, a car speeds
up uniformly from a speed of
12 ms-1 to 27 ms-1.
Calculate its acceleration.
Working:
Therefore:
a =
▲v
▲t
▲v = 27 - 12
= 15 ms-1
▲t = 10 seconds
a =
15
10
= 1.5 ms-2

18. Licensed for use in your school only (© 2009)
Speed – time graphs show
the speed of an object
across time.
Speed (v) is plotted on the
vertical axis and time (t) is
plotted on the horizontal
axis.
Speed – time graphs
What does the slope of the line
represent?
What would a horizontal line on
the graph illustrate?
18SCIENCE 1.4: MOTION
Time
Speed
acceleration
constant speed

19. Licensed for use in your school only (© 2009)
Object at a constant speed
Time
Speed
Object accelerating
Time
Speed
Speed – time graphs
High
acceleration
low
acceleration
How would you calculate the distance travelled by
an object using a speed – time graph?
19SCIENCE 1.4: MOTION
Insert line illustrating
constant speed.

20. Licensed for use in your school only (© 2009)
We are able to calculate
the distance an object
has travelled by working
out the area under its
speed – time graph.
To use this method, you
need to know how to
calculate the area of
basic shapes such as
triangles, squares and
rectangles.
Using your graph to find distance
Area
under the
graph
Time
Speed
20SCIENCE 1.4: MOTION

21. Licensed for use in your school only (© 2009)
Question: speed time graphs
Split the graph into simple shapes, find the area of each
shape, then add areas A, B and C together.
A
B
C
21SCIENCE 1.4: MOTION
Calculate the distance travelled in this short trip:
Jessica’s driving test

22. Licensed for use in your school only (© 2009)
Answer: speed time graphs
Area of rectangle = width x height
Area of a triangle = ½ x base x height
Base
Height
22SCIENCE 1.4: MOTION
Area of A = ½ x 4 x 30
= 60 m
Area of B = 4 x 30
= 120 m
Area of A = ½ x 8 x 30
= 120 m
Total distance travelled = A + B + C
= 300 m

23. Licensed for use in your school only (© 2009)
On a speed – time graph
the slope of the graph
represents the
acceleration of the object.
Do you remember how to
calculate slope?
Calculating acceleration
Time
Speed
y
x
Rise
Run
23SCIENCE 1.4: MOTION
slope =
Rise
=
Change in y-axis
Run Change in x-axis

24. Licensed for use in your school only (© 2009)
Calculating acceleration
A
B
Calculate the (negative) acceleration of the object from A to B
24SCIENCE 1.4: MOTION
acceleration =
10 - 40
=
-30
= -3.75 ms-2
12 - 4 8