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Displacement
Displacement is relative from a point, meaning that the displacement of something
(an object) is its change in position from or toward some point or place.
To understand this concept better, study this example:
A man walks 3 miles east, then turns north and walks 4 miles. What is his
displacement from his starting point?
Solution: Let's start by drawing a diagram, then drawing a straight
line indicating the (which in this case is the shortest direct distance
from the man's final position to his starting position):
First thing perhaps to realize is that displacement is not equal to the man's
distance travelled.
The man travelled a distance of 3 mi + 4 mi = 7 mi.
However, his displacement was only 5 mi (the displacement is the "hypotenuse
of the triangle" whereas the displacement was the sum of its "two legs").
 Related
Topic/Review: Vectors
Velocity
Velocity describes the rate of change of displacement; that is the displacement
experienced over a specified interval of time. Do you remember the old math
equation: Distance=Rate·Time? (D=R·T) If x represents the displacement,
then velocity, v, is equal to x/t, the change of displacement per change
in time. Using SI units, v is expressed in m/s (i.e., [v]=m/s.
There are two "kinds" of velocity:
-
average velocity (vav): the velocity (considered
"constant"--the velocity may not be
constant, but this is the average of all the velocities during the time interval)
throughout a time interval
-
instantaneous velocity (v): the velocity at any one point (or instant) of
time
Acceleration
Acceralation follows in suit with velocity. It measures the change in velocity
over a given time interval. When a car, for example, that is cruising at
a constant speed or velocity or
is at rest (v = 0) has a change in velocity, that is termed either
acceleration or deceleration.
When acceleration is uniform (unchanging or constant during the time interval
in question), the following equations can accurately describe the behavior
of motion:
Coordinate/Position Axes: <x, y>
Arbitrarily, this page shall use x as the horizontal displacement and y as
the vertical displacement. Going forwards (to the right) is +x; backwards
is -x. Going up is -y, and going down is +y Why? This is one way considering
acceleration and deceleration:
When a cannon ball, for example, is shot up straight into the air, it is
initially thrust by the force of the blast. This vi is
relatively large, but the pull of gravity begins to take its effect (pulling
the cannon ball down towards the earth, thus decelerating it because of their
opposite directions), working
against the motion of the cannon ball. The velocity
decreases until it is 0.
The second part of this reasoning is that, because the pull of gravity is
still present, the cannon ball at rest must now fall towards the earth. It's
velocity starts from zero and slowly, by the acceleration (the cannon ball
and gravity are in the same direction) of gravity,
increases until it's final velocity is relatively
large.
|
Legend
|
| vav |
average velocity (the average of the inital and final velocities) |
| vi |
initial velocity (the velocity of an object at the start of the time
interval or distance in question) |
| vf |
final velocity (the velocity of the object at the end of the time interval
or distance in question) |
| t |
time interval, [t] = s (seconds) |
| a |
acceleration, [a] = m/s2 |
| x |
a length or displacement, [x] = m |
| Equation |
Variables Involved |
Variable(s) Not Involved |
v = x
t |
v, x, t |
a, vi, vf |
v = vi + vf
2 |
vi, vf |
a, t |
| vf = vi + at |
vi, vf, a, t |
x |
| x = vit + at2 |
vi, x, a, t |
vf |
| vf2 =
vi2 + 2ax |
vi, vf, a, x |
t |
Freefall
Freefall is (as you may have guessed) vertical acceleration, with common
physics examples like parachuting, dropping bricks from the top of buildings,
cannon shooting, bomb deployment, golf balls falling in a vacuum, water dripping,
etc.
It is a major assumption in freefall motion that when things are falling,
there is no drag caused by air molecules (i.e., air resistance) -->
They are presumed to be falling in a vacuum largely for the sake of convenience
in concept.
In this vacuum-fall situation, the accelerations of any object, comparatively
heavier or lighter than another will be the same. Thus they fall together.
A common example: A rock and a feather are falling in a vacuum. Which one
reaches the ground first?
Solution: They reach it at the same time because their accelerations
are the same, regardless of their weights.
The equations that describe this up and down acceleration are similiar in
nature and form to the general ones (y = x). |
 |
Motion Graphs
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