contents licensed for use in your school only (© 2009) 2 science 1.6 motion defining motion...
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Motion
Contents
Licensed for use in your school only (© 2009)
2SCIENCE 1.6 MOTION
Defining motion
Distance
Time
Speed / velocity
Average speed
Instantaneous speed
Distance – time graphs
Acceleration
Speed – time graphs
Calculating distance
Calculating acceleration
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Something is in motion if its position is changing.
There are four quantities related to motion:
• distance• speed• time• acceleration
Defining motion3SCIENCE 1.4: MOTION
Class discussion
Write a short paragraph describing the movement of an object using the four quantities related to motion. Be creative!!
e.g. The helicopter swooped down the gorge at an incredible speed, it accelerated past the…
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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)5SCIENCE 1.4: MOTION
1km = 1000m
1m = 100cm
How many metres is it from Porirua to Palmerston North?
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Time refers to how long a journey or activity takes.
It is usually measured in:• seconds (s)• minutes (min)• hours (hr)
Time (t)6SCIENCE 1.4: MOTION
Answer:2.7 hours
1 hour = 60 minutes
1 minute = 60 seconds
How many hours is 162 minutes?
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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:
7SCIENCE 1.4: MOTION
km/hr km.hr-1
or
m/s ms-1
Class discussion
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?
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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
This equation can be placed
in a magic triangle
9SCIENCE 1.4: MOTION
Average speed = distance
time
vav = d
t
t = d
vd = v x t
Write the equations to calculate distance (given speed and time) and time (given speed and distance).
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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
vd
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
10SCIENCE 1.4: MOTION
t = d
v
= 400m
5ms-1
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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.
11SCIENCE 1.4: MOTION
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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 D
ista
nce
What would a horizontal line on the graph represent?
12SCIENCE 1.4: MOTION
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Stationary object
• Time
•D
ista
nce
Constant speed
• Time
•D
ista
nce
Distance – time graphs
Vehicle 1
Vehicle 2
13SCIENCE 1.4: MOTION
Answer: Vehicle 1 is moving more quickly.Which vehicle in graph two is moving more quickly?
Graph one Graph two
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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 D
ista
nce
y-axis
x-axis
Rise
Run
14SCIENCE 1.4: MOTION
slope = Rise
=Change in y-axis
Run Change in x-axis
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Question:
A
B
Calculate the speed of the object between A and B
Rise = 40 - 10
Run = 6 - 2
15SCIENCE 1.4: MOTION
Time (s)
speed = 40-10
=30
= 7.5ms-1
6-2 4
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Accelerating object
• Time
•D
ista
nce
Decelerating object
• Time
•D
ista
nce
Curved distance – time graphs
Deceleration is also referred to as ‘negative acceleration’.
16SCIENCE 1.4: MOTION
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Question:
A
B
CD
17SCIENCE 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.
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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
18SCIENCE 1.4: MOTION
Acceleration = change in speed
change in time
a = ▲v
▲t
▲t
What will the magic triangle
look like?
QuestionIn 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
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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?
20SCIENCE 1.4: MOTION
Time
Sp
eed
acceleration
constant speed
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Object at a constant speed
• Time
•S
pe
ed
Object accelerating
• Time
•S
pee d
Speed – time graphs
High acceleration
low acceleration
How would you calculate the distance travelled by an object using a speed – time graph?
21SCIENCE 1.4: MOTION
Insert line illustrating constant speed.
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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
Sp
eed
22SCIENCE 1.4: MOTION
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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
23SCIENCE 1.4: MOTION
Calculate the distance travelled in this short trip:
Jessica’s driving test
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Answer: speed time graphs
Area of rectangle = width x heightArea of a triangle = ½ x base x height
Base
He
igh
t
24SCIENCE 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
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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 S
pee
d
y
x
Rise
Run
25SCIENCE 1.4: MOTION
slope = Rise
=Change in y-axis
Run Change in x-axis
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Calculating acceleration
A
B
Calculate the (negative) acceleration of the object from A to B
26SCIENCE 1.4: MOTION
acceleration = 10 - 40
=-30
= -3.75 ms-2
12 - 4 8
27SCIENCE 1.6 MOTION
Practical: down the rampAim:
To determine the relationship between the steepness of a hill and the speed of a rolling ball.
Equipment:
Retort stand ; clamp ; marble ; metre ruler with channel ; stopwatch.
Method:
1. Set up equipment as shown.
2. Measure the time taken for the marble to roll down the ruler.
3. Test 5 different heights.
4. Record your results in a table.
Instructions: What variables need to be controlled?
How will you ensure that your results are reliable?
Hei
ght (
cm)
retort stand
ruler
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