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Mechanics
Topic 2.1 Kinematics
Kinematics Concepts
Displacement is a vector quantity
Is a measured distance in a given direction
It tells us not only the distance of the object
from a particular reference point but also the
direction from that reference point
In many situations it is measured from the
origin of a Cartesian co-ordinate system
Kinematics Concepts
Speed
Is the rate of change of distance
Or the distance covered per unit time
Speed is the total distance (s) covered
in total time (t)
Speed (v) = total distance (s)
total time (t)
Kinematics Concepts
Velocity
Is the rate of change of displacement
Is a measured speed in a given
direction
It is a vector quantity
Average Velocity
Defined as the total displacement (s) of
the object in the total time (t)
Velocity (vav) = total displacement (s)
total time (t)
vav = s
t
Where  indicates a small change in the
value
Instantaneous Velocity
Is the velocity at any one instant
v = s
t
Where t is tending towards zero
Kinematic Concepts
Acceleration is the rate of change of velocity
in a given direction
a = v / t (where v = v – u)
It is a vector quantity
If the acceleration of an object is positive
then we understand its rate of change of
velocity to be positive and it could mean that
its speed is increasing
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Do not think of acceleration as a ´slowing up´or a
´getting faster´.
Graphical Representation of
Motion
These come in 4 forms
1. Distance-time graphs
2. Displacement-time graphs
3. Velocity-time graphs
4. Acceleration-time graphs
Gradients of Graphs
Gradient of a Displacement-time graph
is the velocity (instantaneous or
average)
Gradient of a Velocity-time graph is the
acceleration (instantaneous or average)
Areas Under Graphs
Area under a Velocity-time graph is the
displacement
Area under a Acceleration-time graph is
the velocity
Areas can be calculated by the addition
of geometric shapes
Uniformly Accelerated Motion
Velocity and hence Acceleration can be
measured using
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Light gates
Strobe photographs
Ticker tape timers
Motion detectors
Air tables
The 4 Equations of Uniformly
(i.e. constant)Accelerated Motion
Aka the “suvat” equations
s=displacement
u=initial velocity
v=final velocity
a=acceleration
t=time
The 4 Equations
Suppose the velocity of a body increases from
u to v in time t, then the uniform
acceleration, a is given by
a = change of velocity
time taken
a=v–u
t
 v = u + at
- equation (1)
Since the velocity is increasing steadily, the
average velocity is the mean of the initial and
final velocities, i.e.
Average velocity = u + v
2
If s is the displacement of the body in time t,
then since average velocity =
displacement/time = s/t
We can say s = u + v
t
2
 s = ½ (u + v) t
- equation (2)
But v = u + at
 s = ½ (u + u + at) t
 s = ut + ½at2
- equation (3)
If we eliminate t from (3) by
substituting in t = (v – u)/a from (1),
we get on simplifying
v2 = u2 +2as
- equation (4)
Knowing any three of s, u, v, a, t, and
the others can be found
Acceleration Due to Gravity
Experiments show that at a particular place
all bodies falling freely under gravity, in a
vacuum or where air resistance is negligible,
have the same constant acceleration
regardless of their masses.
This acceleration towards the surface of the
Earth, known as the acceleration due to
gravity, is denoted by g.
Its magnitude varies slightly from place
to place on the Earth´s surface and is
approximately 9.81 ms-2
The Effects of Air Resistance
Air resistance depends on 2 things
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Surface area
Velocity
Air resistance increases as surface area
increases
Air resistance increases as the velocity
increases
Terminal Velocity
As an object falls through the air, it
accelerates, due to the force of attraction of
the Earth. This force does not change.
As the velocity increases, the air resistance,
the force opposing the motion, increases,
therefore the acceleration decreases.
If the object falls for a long enough time,
then the air resistance (a force acting
upwards) will equal the force of attraction of
the Earth (the weight) (a force acting
downwards)
Now there are no net forces acting on the
object (since the two forces balance) so it no
longer accelerates, but travels at a constant
velocity called its terminal velocity.
Terminal velocity depends on
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The size
Shape
And weight of the object
A sky diver has a terminal velocity of more
than 50 ms-1 (100 miles per hour)
Relative Motion
If you are stationary and watching things
come towards you or away from you, then
determining relative velocities is
straightforward since your frame of reference
is at rest.
If, however, you are in motion, either
towards or away from an object in motion,
then your frame of reference is moving and
relative velocities have to be determined from
vector addition or subtraction.
In this case the relative velocity is the
velocity of the object relative to your
motion.
Examples include
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cars overtaking
Trains going passed platforms