Mechanics - The Study of Motion
Kinematics - Describing Motion
In this unit we will be using some new vocabulary and math techniques to
describe motion. In the first part of the unit we will do this all
in one dimension. In the second part we will add the concept of vectors
to describe motion in two dimensions. All we are concerned with at
this time is describing motion, not the causes of motion. The causes
of motion will come later.
Vocabulary:
Displacement: Many people think of displacement as distance. As
is common in science words have very specific meanings and those meanings
may not be the same as in general society. Distance is the measurement
of space between two points. Nothing has to happen for there to be
a distance. Displacement requires movement, a change in position, an
object going from one place to another. Direction is required for displacement
but the direction is often assumed or implied. Displacement in the
metric system is measured in meters and the symbol in the math equations
that we use is s.
Velocity: Velocity is the slope of the displacement vs. time graph.
Many people think of velocity as speed. The major difference
is that velocity has direction as part of the measurement, either expressed
( 20 m/s North) or implied (falling at 3.2 m/s). For people with higher
math skills, velocity is the rate of change in position or the first derivative
of position. Velocity in the metric system is measured in meters/second
and the symbol in the math equations we use is v.
Acceleration: Acceleration is the slope of the velocity vs. time
graph. Acceleration always has direction although in common usage
people often us deceleration as a term for negative acceleration. It
is the second derivative of position or the rate of change of velocity.
Acceleration is measured in meters/second/second (meters per second
squared) and the symbol in the math equations we use is a.
Jerk: The jerk is a physics quantity that is seldom used in formal
physics but the concept is often used in general society. The jerk
is the slope of the acceleration vs. time graph. Because any measurement
errors are already greatly magnified in acceleration, calculating a value
for jerk often results in errors that are greater than the values calculated.
Time: Something that we all know about but is difficult to define.
In classical physics the change in time is constant. We may define
the beginning of time how ever we want but time does not stop, speed up, slow
down or end. Time in the metric system is measured in seconds and the
symbol in the math equations we use is t.
Slope: Many people define slope as "the rise over the run". While
this is a true statement I think it loses much of the beauty of the math.
Slope as a formula is calculated as (y2-y1)/(x2-x1).
Producing graphs and being able to estimate the slope of the graph are
great tools to get a "big picture" view of the motion of objects. It
is also an abstract thinking skill that takes many students a long time to
master. A major focus on the first part of this unit will be on creating
and analyzing these graphs.
Independent variable: In this section of physics, time is always the independent variable, the quantity
that does not depend on anything else. In classic math, the independent
variable is always put on the x axis.
Dependent variable: The variables that are determined by something
else. In the case of kinematics the independent variables depend on
time. Where you are, how fast you are moving, how your velocity is
changing all depend on time, the time does not depend on you being somewhere
(can you imagine time ceasing to exist because you weren't in your assigned
seat during 1st block?). The dependent variable is always put on the
y axis.
Math Equations:
average velocity = ∆s/∆t
acceleration = ∆v/∆t sf
= si + vi∆t + 1/2 a∆t2
2a∆s=vf2-vi2
Links:
The Physics Classroom
The Physics Classroom - New Version
Human Kinematics - Future doctors, atheletes, nurses,
physical therapists take note!
Kinematics
Simulation at Thinkquest
Relative Motion Simulator Frame of Reference Demonstrated
Projectile Simulator