Mechanics
Topic 2.1 Kinematics
Kinematic Concepts
Displacement
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
It is a vector quantity
In many situations it is measured from the
origin of a Cartesian co-ordinate system
Kinematic Concepts
Speed
Is the rate of change of distance
Or the distance covered per unit time
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 tells us not only the speed of the
object but also the 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
Gradiants 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 ( Duncan Page 142/3)
Ticker tape timers
The Equations of Uniformly
Accelerated Motion
There are 4 equations which we use
when dealing with constant acceleration
problems
I call them the “suvat” equations
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 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.
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 50ms-1 (100 miles per hour)
Relative Motion
If you are stationary and watching
things come towards you or away from
you, then your stating velocities is easy.
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.
Examples include
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cars overtaking
Trains going passed platforms