Transcript Topic 2.1

Mechanics
Topic 2.1 Kinematics
Kinematic Concepts:
Displacement
Is a measured distance in a given direction
It is a vector quantity
It tells us not only the distance of the object
from a particular reference point but also the
direction from that reference point
Typically, it is measured from the origin of a
Cartesian co-ordinate system
Kinematic Concepts:
Speed
Is the rate of change of distance
Or is the distance covered per unit time
It is a scalar quantity…it has magnitude
only
Speed is the total distance (d) covered
in total time (t)
Speed (s) = total distance (d)
total time (t)
Kinematic Concepts:
Velocity
Is the rate of change of displacement
Is a measured speed in a given
direction
It is a vector quantity…It tells us not
only the speed of the object but also
the direction
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 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
Acceleration in the same direction as motion
results in an increase in speed
Acceleration in the opposite direction as
motion results in a decrease in speed
Acceleration perpendicular to the direction of
motion results in a change in direction
Graphical Representation of
Motion
These come in 5 forms…
1. Distance-time graphs
2. Displacement-time graphs
3. Speed-time graphs
4. Velocity-time graphs
5. Acceleration-time graphs
Gradiants of Graphs
Gradiant of a Displacement-time graph
is the velocity
Gradiant of a Velocity-time graph is the
acceleration
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
The Equations of Uniformly
Accelerated Motion
There are 4 equations which we use
when dealing with constant acceleration
problems
You need to be able to derive them
The 4 Equations
Supposing 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
irrespective of their masses.
This acceleration towards the surface of the
Earth, known as the acceleration due to
gravity, is donated by g.
Its magnitude varies slightly from place
to place on the Earth´s surface and is
approximately 9.8ms-2

The IB generally allows for an approximation of 10 ms-1 to
be used
All of the uniform acceleration equations are
applicable to situations of free fall
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 long enough, 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.
A sky diver has a terminal velocity of more
than 50ms-1 (100 miles per hour)
Relative Motion
If you are stationary and watching
things come towards or away from you,
then your stating of velocities is
straightforward.
If, however you are in motion, either
moving towards or away from an object
in motion, then your frame of reference
is different
In this case the relative velocity is the
velocity of the object relative to your
motion.
Common examples include
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
cars overtaking
Trains going passed platforms