####
Terms

**
Kinematics
** -
Kinematics is concerned with describing the way in which objects move.

**
Displacement
** -
An object's 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 graviational 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/s^{2}.

**
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.

**
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*) = |