When an object all of a sudden changes
its velocity and /or direction, we can always find an
interaction between that object and its surroundings
that is responsible for this change. We say that the
surroundings exert a force on the object. Under the
influence of the force, the object will accelerate. By the
law of forces together with the properties of the body
and its environment, we can calculate the force acting
on the object. The laws of motion are then used to
calculate the acceleration of the object under influence
of these forces.
The study of
motion is called
kinematics. The word kinematics comes from the Greek
word **kinema**, meaning motion. Kinematics is the
science of motion. Kinematics describes the positions
and motions of objects in space as a function of time
but does not consider the causes of motion. In human
movement, it is the study of the positions, angles,
velocities, and accelerations of body segments and
joints during motion. Precisely, kinematics
involves position, velocity and acceleration (and their
rotational equivalents).
Mathematically, the exact characteristic of the motion
of objects is expressed by the shape and the slope of
the lines on a position versus time. While an object is
in motion, the velocity of the object and the rate of
change of velocity per unit time at each point in time
are necessary. We will introduce three important
concepts related to motion: position, velocity, and
acceleration.
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**Position**
The first concept needed in depicting the motion of
an object is its **position** relative to some fixed
reference point. Position is the point in space that an
object occupies, this needs to be defined in some
coordinate system. This involves two issues: the **
distance** the object is away from a reference point,
and also the **direction** relative to that reference
point. The position is therefore a vector quantity since
it has both a magnitude (the distance) and a direction.
Occasionally we wish to talk about the position of an
object relative to its starting point at some initial
time. This is called the **displacement** of the
object. Displacement may also be defined as the straight
line distance between the initial position *x*_{i}
and final position *x*_{f} of the body. The
net change in position (displacement) is given by
The symbol
D
is used to indicate a change in position *x*.
Mathematically, position is a **
function**
that can be either scalar-valued *x*(*t*) (for
motion in one dimension) or vector-valued
**x**(*t*)
(for motion in two or three dimensions). At each point
in time its value represents the position of an object
at a particular time.
**Velocity**
For an
object in motion the function of **velocity** is
important. This function is the time derivative of the
position function and gives the velocity of an object at
each point in time. Note that, as with the position, the
velocity is a vector: it has a magnitude and a direction
associated with it.
Sometimes
only the magnitude of the velocity is of interest. It is
then called the **speed**, which is the most basic
property of a moving body. The speed is the ratio of the
distance traveled to the time required from the travel.
The average speed is defined as the total distance, *s*,
traveled during a particular time divided by that time
interval, *t*
If the average
speed is the same for all parts of a trip, then the
speed is constant.
Example: Velocity-time graph
**Acceleration**
Acceleration *a*(*t*) is a very
important concept in Newtonian physics. Just as the
velocity involves a rate of change of position in time,
the **acceleration** of an object describes the rate
of change of velocity per unit time, and is hence
usually given in units such as m/s^{2}.
Therefore, an object whose velocity is changing is said
to be accelerating. Following a similar approach as
before, we define the average acceleration *a*_{ave},
as the change in velocity divided by the time required
for the change. It may be defined as
or in symbol
where *v*_{2} is the final
velocity and *v*_{1} is the initial
velocity. Simple algebra gives
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Example: Deceleration |