Introduction to Kinematics
Kinematics Terms
Terms
Kinematics
-
Kinematics is concerned with describing the way in which objects move.
Displacement
-
An objects total change in position. If a man runs around an oval 400 meter track, stopping at the precise location he began, though he ran a distance of 400 meters, his total displacement was 0.
Dynamics
-
Dynamics focuses on understanding why objects move the way they do.
Reference frame
-
The coordinate system with respect to which motion is being described.
Speed
-
A measure of how fast an object is moving.
Average velocity
-
The time-average of the velocity function over a specified time-interval.
(See formula below.)
Instantaneous velocity
-
The value of the velocity function at a particular instant in time. (See
formula below.)
Gravitational acceleration
-
The gravitational acceleration of objects near the earth's surface is the
same
for all objects regardless of mass and is given by the number
g = 9.8m/s2
.
Scalar-valued function
-
A function that outputs scalars (regular
numbers). Most common functions that you are probably familiar with are
scalar-valued functions.
Vector-valued function
-
A function that outputs vectors. This means that
while the domain of the function may consist of
scalars, the values in the range are all vectors.
Position function
-
A position function can be either scalar-valued (for motion in one
dimension) or vector-valued (for motion in two or three dimensions). At
each point in time its value represents the position of an object at that time.
Velocity function
-
This function is the time-derivative of the position function, and
gives the velocity of an object at each point in time.
Acceleration function
-
This function is the time-derivative of the velocity function, and the
second time-derivative of the position function. It gives the value of the
acceleration of an object at each point in time.
Time-derivative
-
The time-derivative of a function is a new function whose value at each
point represents the rate of change of the original function with respect
to time.
Simple harmonic motion
-
Periodic motion that can be described by special types of position functions.
Examples of simple harmonic motion include an object moving in a circle and a
ball bouncing up and down on a spring.
Formulae
| The average velocity for an object with position function x(t) over the time interval (t 0, t 1) . |
v
avg = 
|
| The instantaneous velocity at time t for an object with position function x(t) . |
v(t) = 
|
