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Science

Kinematics

This is about how things move in a straight line or more scientifically how things move in
one dimension. This is useful for learning how to describe the movement of cars along a straight
road or of trains along straight railway tracks. If you want to understand how any object moves,
for example a car on the freeway, a soccer ball being kicked towards the goal or your dog chasing
the neighbour’s cat, then you have to understand three basic ideas about what it means when
something is moving. These three ideas describe different parts of exactly how an object moves.
They are:

1. position or displacement which tells us exactly where the object is,

2. speed or velocity which tells us exactly how fast the object’s position is changing or more
familiarly, how fast the object is moving, and

3. acceleration which tells us exactly how fast the object’s velocity is changing.
You will also learn how to use position, displacement, speed, velocity and acceleration to describe
the motion of simple objects. You will learn how to read and draw graphs that summarise the
motion of a moving object. You will also learn about the equations that can be used to describe
motion and how to apply these equations to objects moving in one dimension.

Distance and Displacement 

Definition: Displacement
Displacement is the change in an object’s position. The displacement of an object is defined as its change in position (final position minus initial position). Displacement has a magnitude and direction and is therefore a vector. For example, if the initial position of a car is xi and it moves to a final position of xf , then the displacement is:
xf − xi
However, subtracting an initial quantity from a final quantity happens often in Physics, so we
use the shortcut ∆ to mean final – initial. Therefore, displacement can be written:
∆x = xf − xi
Important: The symbol ∆ is read out as delta. ∆ is a letter of the Greek alphabet and is
used in Mathematics and Science to indicate a change in a certain quantity, or a final value
minus an initial value. For example, ∆x means change in x while ∆t means change in t.

Important: The words initial and final will be used very often in Physics. Initial will always
refer to something that happened earlier in time and final will always refer to something
that happened later in time. It will often happen that the final value is smaller than the
initial value, such that the difference is negative. This is ok!

Definition: Vectors and Scalars
A vector is a physical quantity with magnitude (size) and direction. A scalar is a physical
quantity with magnitude (size) only.

The differences between distance and displacement can be summarised as:
Distance
1. depends on the path
2. always positive
3. is a scalar
Displacement
1. independent of path taken
2. can be positive or negative
3. is a vector

Speed, Average Velocity and Instantaneous Velocity

Definition: Velocity
Velocity is the rate of change of position.

Definition: Instantaneous velocity
Instantaneous velocity is the velocity of an accelerating body at a specific instant in time.

Definition: Average velocity
Average velocity is the total displacement of a body over a time interval.

Velocity is the rate of change of position. It tells us how much an object’s position changes in
time. This is the same as the displacement divided by the time taken. Since displacement is a
vector and time taken is a scalar, velocity is also a vector. We use the symbol v for velocity. If
we have a displacement of ∆x and a time taken of ∆t, v is then defined as:
velocity (in m · s−1 ) =
v =  change in displacement (in m) / change in time (in s)   or = ∆x / ∆t

Velocity can be positive or negative. Positive values of velocity mean that the object is moving
away from the reference point or origin and negative values mean that the object is moving
towards the reference point or origin.
Important: An instant in time is different from the time taken or the time interval. It
is therefore useful to use the symbol t for an instant in time (for example during the 4th
second) and the symbol ∆t for the time taken (for example during the first 5 seconds of
the motion).

Average velocity (symbol v) is the displacement for the whole motion divided by the time taken
for the whole motion. Instantaneous velocity is the velocity at a specific instant in time.
(Average) Speed (symbol s) is the distance travelled (d) divided by the time taken (∆t) for
the journey. Distance and time are scalars and therefore speed will also be a scalar. Speed is
calculated as follows:
speed (in m · s−1 ) =  distance (in m) / time (in s)  or = d / ∆t
Instantaneous speed is the magnitude of instantaneous velocity. It has the same value, but no
direction.

Differences between Speed and Velocity
The differences between speed and velocity can be summarised as:
Speed
1. depends on the path taken
2. always positive
3. is a scalar
4. no dependence on direction and
so is only positive

Velocity
1. independent of path taken
2. can be positive or negative
3. is a vector
4. direction can be guessed from the sign (i.e. positive or negative)

Additionally, an object that makes a round trip, i.e. travels away from its starting point and then
returns to the same point has zero velocity but travels a non-zero speed.

Acceleration 

Definition: Acceleration
Acceleration is the rate of change of velocity.

Acceleration (symbol a) is the rate of change of velocity. It is a measure of how fast the velocity
of an object changes in time. If we have a change in velocity (∆v) over a time interval (∆t),
then the acceleration (a) is defined as:

acceleration (in m · s−2 ) = change in velocity (in m · s−1 ) / change in time (in s)
a= ∆v / ∆t

Since velocity is a vector, acceleration is also a vector. Acceleration does not provide any infor-
mation about a motion, but only about how the motion changes. It is not possible to tell how
fast an object is moving or in which direction from the acceleration.

Like velocity, acceleration can be negative or positive. We see that when the sign of the acceler-
ation and the velocity are the same, the object is speeding up. If both velocity and acceleration
are positive, the object is speeding up in a positive direction. If both velocity and acceleration
are negative, the object is speeding up in a negative direction. If velocity is positive and accel-
eration is negative, then the object is slowing down. Similarly, if the velocity is negative and the
acceleration is positive the object is slowing down.

Important: Acceleration does not tell us about the direction of the motion. Acceleration
only tells us how the velocity changes.

Important: Deceleration
Avoid the use of the word deceleration to refer to a negative acceleration. This word usually
means slowing down and it is possible for an object to slow down with both a positive and
negative acceleration, because the sign of the velocity of the object must also be taken into
account to determine whether the body is slowing down or not.

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About dhaphysics

i am a physics teacher, currently working in dharumavantha school and Maldives polytechnic.

Discussion

5 thoughts on “Kinematics

  1. eba ragalhuvey sir

    Posted by saryf | May 14, 2011, 4:39 am
  2. gud

    Posted by saryf | May 14, 2011, 4:40 am
  3. this post got; simulation and …./ can be taken anything out of these to the exam can’t u?

    Posted by mussad | May 14, 2011, 3:02 pm
  4. thanks for the hard work that u r doing,if study can pass all.

    Posted by absee | May 15, 2011, 10:51 pm

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Good Luck Guyz…

REVISION SESSION TWO IS ON TOMORROW @ 2PM. DON'T MISS THE LECTURE. AND ALSO MAKE SURE YOU MEET THE ATTENDANCE .
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