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Acceleration
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Acceleration
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The acceleration of an object is a measure of how quickly
its velocity changes.
A train accelerates in a
straight line from rest.
As it does, its velocity
increases.
The brakes on this motorcycle
are causing it to slow down.
This is negative acceleration.
Negative acceleration is often
called deceleration.
What is acceleration?
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Acceleration of cars
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Acceleration and direction
Acceleration is a vector quantity. Vector quantities have a
direction as well as a magnitude (size). Scalar quantities
only have magnitude.
This means that acceleration must involve either a change
in speed, a change in direction, or both.
Scalar
quantitiesVector
quantities
Mass
Time
Speed
Velocity
Acceleration
Displacement
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Estimating Acceleration
…a sprinter.
… a speeding roller coaster.
Estimate the acceleration of…
…a bus.
Roughly 50m/s2
About 1m/s2
Around 5m/s2
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Acceleration
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The acceleration of an object can be calculated using
this equation:
change in velocity
time takenacceleration =
Acceleration is measured in metres per second per
second (m/s2). It can be positive or negative.
Like velocity, change in velocity is also measured in
metres per second (m/s). It can be positive or negative.
Time taken is measured in seconds (s).
How is acceleration calculated?
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Simple acceleration problem
A racing car accelerates
from rest to a velocity of
27m/s in 2 seconds.
What is its acceleration?
acceleration =
=
= 13.5m/s2
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acceleration =
Developing the formula
The formula to calculate acceleration can also be written
like this: (v–u)
ta =
v is the final velocity, measured in metres per
second (m/s).
a is acceleration, measured in metres per second
squared (m/s2).
t is the time taken, measured in seconds (s).
u is the initial velocity, measured in metres per
second (m/s).
This formula is the same as:
change in velocity
time taken
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4
A race horse accelerates from 6m/s to a speed of 12m/s in
a time of 4 seconds. What is the horse’s acceleration?
= 1.5m/s2
=
Acceleration problem
(v–u)
ta =
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Using a formula triangle
A formula triangle helps you to rearrange a formula.
The formula triangle for acceleration (a), change in
velocity (v) and time (t) is shown below.
×
Cover the quantity that you are trying to work out. This gives
the rearranged formula needed for the calculation.
So to find acceleration (a),
cover up a……which gives the formula…
a =∆v
t
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A hungry cheetah spots a gazelle and decides to chase it.
The cheetah accelerates at 10m/s2 from rest until it
reaches 20m/s. How long did this take?
acceleration =
=
= 2s
Acceleration problem
time taken =
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Acceleration calculations
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Uniform acceleration
If an object’s acceleration is constant, and it is travelling in
a straight line, then this equation applies:
Acceleration that is not changing is often
referred to as uniform acceleration.
v2 - u2 = 2 a s
v is the final velocity, measured in metres per
second (m/s).
a is acceleration, measured in metres per second
squared (m/s2).
s is the displacement, measured in metres (m).
u is the initial velocity, measured in metres per
second (m/s).
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Acceleration Problem
A cruise ship accelerates from rest at a constant rate and
travels in a straight line out of the harbour. If its final
velocity is 10m/s and the distance from the port to the sea
is 150m, what was its acceleration?
v2 – u2
2s= a
v2 - u2 = 2 a s
Divide both
sides by 2s
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2 x 150
Acceleration Problem
A cruise ship accelerates from rest at a constant rate and
travels in a straight line out of the harbour. If its final
velocity is 10m/s and the distance from the port to the sea
is 150m, what was its acceleration?
= 0.33m/s2
=
v2 – u2
2sa =
100
300=
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Acceleration
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A graph of velocity over time can be used to work out the
acceleration of an object. Acceleration is represented by
the slope of the line - the gradient.
If the gradient goes
up, the object has a
positive acceleration.
If the gradient goes down, the
object has a negative
acceleration, or deceleration.
Calculating acceleration from the gradient
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Analyzing velocity–time graphs
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What’s the acceleration?
What is the acceleration of the object between points
A and B?
The object’s velocity has increased by 20m/s
(25 – 5 = 20).
It took 4s to change
speed (6 – 2 = 4).
acceleration =
=
= 5m/s2
velocity
time
20
4
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Calculating acceleration from a graph
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In a velocity—time graph, the
distance along the y axis (i.e.
the height of the rectangle)
represents the velocity of the
object.
The area under a velocity–time graph
area = height × width
The distance along the x axis
(i.e. the width of the rectangle)
represents the time taken.
What does the area underneath a velocity—time
graph represent?
Therefore, the area of the rectangle is equivalent to the
velocity multiplied by the time.
area = velocity × time
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The area under a velocity–time graph
What does the area underneath a velocity—time
graph represent?area = velocity × time
Remember that:
velocity = distance
time
Which rearranges to give
distance = velocity × time
Therefore:
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The area under a velocity–time graph
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DIY velocity–time graph
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Acceleration and direction
Remember: both velocity and acceleration are vector
quantities. Therefore, in order to graph how velocity
changes over time, the direction the object is moving in
needs to be taken into account.
As a person goes down this water
slide, how does their acceleration
affect their velocity in the direction
of the arrow?
One way of doing this is to specify the direction first,
and only think about how the velocity changes
in that particular direction.
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Velocity–time graphs
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Acceleration
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Acceleration through a fluid
When objects accelerate through a medium (like air or
water) they displace the molecules already present. This
produces a resistive force.
The faster an object is moving,
the greater the resistive force
becomes.
Liquids tend to have a higher
resistive force than gases.
Imagine trying to run underwater
compared to running on land.
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Acceleration due to gravity
Gravity is a force that acts to
attract masses to one another.
Close to the Earth’s surface, gravitational forces create an
acceleration of about 9.8m/s2.
Consider an object dropped from a
plane. The force of gravity
accelerates the object downwards.
As its speed increases, so does the air
resistance. Eventually, the two forces
balance, and the object has reached
terminal velocity.
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Terminal velocity of a skydiver
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Velocity–time graph of skydiver
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How does a parachute work?
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Acceleration
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What does the graph show?
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Glossary
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Multiple-choice quiz