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→Distance and displacement
= '''Motion in One Dimension''' =
'''
In this unit, we will attempt to understand and describe motion and explain the motion of objects. Kinematics is the science of describing the motion of objects using
words, diagrams, numbers, graphs, and equations.
<br>
We have already seen that the study of Physics is about building models and a framework to explain the phenomena we observe. If we need to build a model, we need to
develop a common vocabulary to describe our observations. Once we have the vocabulary, we can use that to analyze the motion of objects
and ultimately explain how they move in the way they do.
<br>
In this unit, we will attempt to
In this unit, we will study Motion in One Dimension and the equations of motion that describe the case of motion with uniform acceleration.
<br>
= '''Concept Map''' =
<br>
<br>
This concept map needs some work. Please refine it and share on the mathssciencestf@googlegroups.com.
<br>
= '''Distance and displacement''' =
<br>
<br>
In the world around us, we see different objects around us. What would be one of the first observations you would make about an object? The first thing we
would notice (other than the shape, size, color, etc.) is whether it is moving or at rest. We often perceive motion (movement) when
something changes its position with respect to time. Alternatively, we can infer that something has moved after observing its
surroundings. Can you think of examples that describe both these?
<br>
When we begin to describe motion, the first thing that comes to mind is that of direction. It is not enough to know that something has moved; it is equally important to
know where it has moved. There are many quantities in Physics that get their relevance from the direction in which they are operating.
When we begin to describe motion,
the first thing that comes to mind is that of direction. It is not
enough to know that something has moved; it is equally important to
know where it has moved. There are many quantities in Physics that
get their relevance from the direction in which they are operating.
<br>
<br>
When a quantity can be described
When a quantity can be described just by its magnitude, it is called a scalar. For instance, mass. It is not very meaningful to say, that body A has mass 20 kg in the
just by its magnitude, it is called a scalar. For instance, mass.
eastern direction. On the other hand, I do need to know which is the path to take from Town A to Town B. The description of the path from
It is not very meaningful to say, that body A has mass 20 kg in the
eastern direction. On the other hand, I do need to know which is the
path to take from Town A to Town B. The description of the path from
A to B is meaningful when I know the direction of travel.
A to B is meaningful when I know the direction of travel.
* ''Scalars are quantities which are fully described by a magnitude (or numerical value) alone. Mass, volume, area, temperature, etc. are scalars.''
''* ''Scalars are quantities which are fully described by a magnitude (or numerical value) alone. Mass, volume, area, temperature, etc. are scalars.''
* ''Vectors are quantities which are fully described by both a magnitude and a direction.''
''* ''Vectors are quantities which are fully described by both a magnitude and a direction.''''
* ''Rest : When a body does not change its position with respect to surroundings, then it is said to be in a state of rest.''
* ''Rest : When a body does not change its position with respect to surroundings, then it is said to be in a state of rest.''
* ''Motion: When a body changes its position with respect to surroundings, then it is said to be in a state of motion.''
* ''Motion: When a body changes its position with respect to surroundings, then it is said to be in a state of motion.'''
This notion of rest and motion is
This notion of rest and motion is
uniform, non-uniform, etc.
uniform, non-uniform, etc.
* ''Distance: Distance is the length of the path traveled in a certain time. ''
* ''Distance: Distance is the length of the path traveled in a certain time. ''
* ''D '''A''' isplacement: Displacement is the shortest distance between the initial and final position.''
* ''Displacement: Displacement is the shortest distance between the initial and final position.''
[[Image:Motion%20in%20One%20Dimension_html_m497999.png]]
[[Image:Motion%20in%20One%20Dimension_html_m497999.png]]
her effective displacement from the initial position, A, is zero.</u>''
her effective displacement from the initial position, A, is zero.</u>''
<br>
<br>
Since, we are only interested in
Since, we are only interested in
the initial and final positions for displacement, we are interested
the initial and final positions for displacement, we are interested
the direction in which the displacement occurs. Also associated with
the direction in which the displacement occurs. Also associated with
the idea of displacement is the notion of a reference point, the
the idea of displacement is the notion of a reference point, the
initial position with respect to which the displacement occurs.
initial position with respect to which the displacement occurs.
<br>
<br>
Motion can occur in a number of
Motion can occur in a number of
complex ways – straight line, circular, or any combination thereof.
complex ways – straight line, circular, or any combination thereof.
We will discuss in this module straight line and circular motion.
We will discuss in this module straight line and circular motion.
<br><br>
= Speed and velocity =
= Speed and velocity =
* ''Velocity is defined as (final position – initial position)/ time taken. Velocity is a vector quantity and needs both magnitude and direction. ''
* ''Velocity is defined as (final position – initial position)/ time taken. Velocity is a vector quantity and needs both magnitude and direction. ''
* ''Velocity describes the speed and the direction in which the motion has o[[Image:Motion%20in%20One%20Dimension_html_m30eb9e7a.png]]ccurred.''
* ''Velocity describes the speed and the direction in which the motion has occurred.[[Image:Motion%20in%20One%20Dimension_html_m30eb9e7a.png]]''
<br>
When evaluating the velocity of
When evaluating the velocity of
an object, one must keep track of direction. It would not be enough
an object, one must keep track of direction. It would not be enough
'''----------------------------------------------------------'''
'''----------------------------------------------------------'''
= Rate of change of velocity =
= Rate of change of velocity =
[[Image:Motion%20in%20One%20Dimension_html_3f0db0d0.png]] Let
us go back to our Physics teacher walking along the boundary. She
us go back to our Physics teacher walking along the boundary. She
may cover 4m East in 2 seconds; 2m South in 2 seconds, 4 m West in 4
may cover 4m East in 2 seconds; 2m South in 2 seconds, 4 m West in 4
A moving object may not always
A moving object may not always move at the same rate not does it always have to move at variable
move at the same rate not does it always have to move at variable
rates. An object moving at constant velocity is an example of
rates. An object moving at constant velocity is an example of
uniform motion. Velocity varies with time in non-uniform motion.
uniform motion. Velocity varies with time in non-uniform motion.
<br>
<br>
Once we know that an object has a
Once we know that an object has a
<br>
<br>
The acceleration can be uniform or non-uniform.
The acceleration can be uniform
Uniform acceleration means the velocity changes at
or non-uniform. Uniform acceleration means the velocity changes at
the same rate. Non-uniform acceleration means velocity does not change at a uniform rate.
the same rate. Non-uniform acceleration
means velocity does not change at
a uniform rate.
<br>
<br>
<u>What is the direction of the
<u>What is the direction of the acceleration vector?</u>
acceleration vector?</u>
If an object is moving in a line
If an object is moving in a line and its speed is increasing, the change in velocity is positive. The
and its speed is increasing, the change in velocity is positive. The
acceleration in this case is adding to the velocity and is considered
acceleration in this case is adding to the velocity and is considered
to be positive and in the same direction as then velocity vector.
to be positive and in the same direction as then velocity vector.
What happens when you pedal faster on a bicycle?
What happens when you pedal faster on a bicycle?
<br>
<br>
{| border="1"
{| border="1"
|-
|-
<br>
<br>
|
|
|
|}
|}
Which
Which one of these tables represent positive acceleration?
If an object is moving in a line and its speed is decreasing,
the change in velocity is negative. The acceleration in this case is
the change in velocity is negative. The acceleration in this case is
reducing the velocity and is considered to be negative and in the
reducing the velocity and is considered to be negative and in the
1. In everyday life, you come
1. In everyday life, you come across a range of motions in which
across a range of motions in which
2. Starting from a stationary
2. Starting from a stationary position, Rahul pedals his bicycle to attain a velocity of 6 m/s in
position, Rahul pedals his bicycle to attain a velocity of 6 m/s in
30 seconds. Then he applies the brakes in such a way that the
30 seconds. Then he applies the brakes in such a way that the
velocity of the bicycle comes down to 4 m/s in the next 5 seconds.
velocity of the bicycle comes down to 4 m/s in the next 5 seconds.
happen to the velocity as it falls, ignoring any air resistance?
happen to the velocity as it falls, ignoring any air resistance?
= '''Graphs to represent the above quantities''' =
= Graphs to represent the above quantities =
<u>'''Distance time graphs'''</u>
<u>'''Distance time graphs'''</u>
So far, we have examined several
So far, we have examined several
terms concepts associated with one dimensional motion. It is easier
terms concepts associated with one dimensional motion. It is easier
<br>
<br>
[[Image:Motion%20in%20One%20Dimension_html_3177b276.gif]]
[[Image:Motion%20in%20One%20Dimension_html_3177b276.gif]]
The position of the object is plotted for time from 0 to 5
seconds. The position is at 5 units all through the 5 seconds.
seconds. The position is at 5 units all through the 5 seconds.
<br>
<br>
Has the object moved?
Has the object moved? What is its velocity?
What is its velocity?
Considerthe object below.
<br>[[Image:Motion%20in%20One%20Dimension_html_m2e3ee2d5.gif]]
The object is staring from 0;
The object is staring from 0;jumps to 10 m at t = 1 second and stays there till t = 2 seconds;
jumps to 10 m at t = 1 second and stays there till t = 2 seconds;
jumps upto 20 m at t = 2 seconds and so on.
jumps upto 20 m at t = 2 seconds and so on.
<br>
<br>
Instead of jumping in steps if the object were to move continuously, the position time graph would
Instead of jumping in steps if
the object were to move continuously, the position time graph would
like the one below.
like the one below.
A
A straight line means a uniform slope.
Slope = y<sub>2</sub> – y<sub>1</sub> / x<sub>2</sub> = x<sub>1 </sub>
= change in position/ change in time
= velocity
The object is covering equal distances in equal intervals of time; what
can you say about the velocity?
<br>
<br>
[[Image:Motion%20in%20One%20Dimension_html_714365d4.png]]<br>
[[Image:Motion%20in%20One%20Dimension_html_714365d4.png]]<br>
[[Image:Motion%20in%20One%20Dimension_html_68367353.gif]]<br>
[[Image:Motion%20in%20One%20Dimension_html_68367353.gif]]<br>
In this graph, the object is
In this graph, the object is moving uniformly till t = 3 seconds, when it covers a distance of 2m. After that, it stays at rest.
moving uniformly till t = 3 seconds, when it covers a distance of 2
<br>
<br>
Can there be a position – time
Can there be a position – time graph parallel to the y-axis? Why or why not?
graph parallel to the y-axis? Why or why not?
<br>
<br>
Considerthe object below.
<br>
<br>
[[Image:Motion%20in%20One%20Dimension_html_m5abddb4f.png]]<br>
[[Image:Motion%20in%20One%20Dimension_html_m5abddb4f.png]]<br>
[[Image:Motion%20in%20One%20Dimension_html_m74cc4a47.png]]<br>
[[Image:Motion%20in%20One%20Dimension_html_m74cc4a47.png]]<br>
[[Image:Motion%20in%20One%20Dimension_html_m21074457.png]]
The object here is moving from position 0 m to 50 m in 5 seconds. But it is not covering the same distance in each second.
<br>
<br>
<br>
Slope = (y<sub>2</sub> – y<sub>1</sub> )/ (x<sub>2</sub> - x<sub>1 </sub>)
= change in position/ change in time
= velocity
= change in position/ change in
The
The rate at which the position is changing is not constant.; this means
rate at which the position is changing is not constant.; this means
that the slope at different points is different. What can you say
that the slope at different points is different. What can you say
about the velocity?
about the velocity?
<br>
<br>
Can you interpret the following position time graphs?
Can
you interpret the following position time graphs?
<br>
<br>
{| border="1"
{| border="1"
In a similar manner, we can also
In a similar manner, we can also plot velocity time graphs to describe motion of a body.
plot velocity time graphs to describe motion of a body.
<br>
<br>
[[Image:Motion%20in%20One%20Dimension_html_27697866.gif]]
the graph below. What can you say about the motion? Is the body
Examine the graph below. What can you say about the motion? Is the body
moving?
moving?
<br>
<br>
Short quiz :
Short quiz :
What is the displacement of the body at the end of 3 seconds?
What is the displacement of the
body at the end of 3 seconds?
* 5
* 5
* 15 m
* 15 m
* Can’t say – not enough information
* Can’t say – not enough information
<br>
<br>
The
The graph describes the motion of a body which moves at a constant
graph describes the motion of a body which moves at a constant
velocity. At each second, the body covers 5m. Therefore, at the end
velocity. At each second, the body covers 5m. Therefore, at the end
of 3 seconds, the displacement would be 15 m.
of 3 seconds, the displacement would be 15 m.
<br>
<br>
Examine carefully the position – time information below.
Examine
carefully the position – time information below.
[[Image:Motion%20in%20One%20Dimension_html_6806e5d0.png]]
[[Image:Motion%20in%20One%20Dimension_html_6806e5d0.png]]
Can
Can you draw a velocity-time graph?
you draw a velocity-time graph?
[[Image:Motion%20in%20One%20Dimension_html_m409e339.gif]]<br>
[[Image:Motion%20in%20One%20Dimension_html_m409e339.gif]]<br>
What
What can you say about the velocity of this body?
can you say about the velocity of this body?
<br>
<br>
Is
Is it uniform, increasing or decreasing?
it uniform, increasing or decreasing?
<br>
<br>
[[Media:Example.ogg]]
