Terms and Formulae
Terms
Kinematics
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Kinematics is concerned with describing the way in which objects move.
Displacement
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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
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Dynamics focuses on understanding why objects move the way they do.
Reference frame
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The coordinate system with respect to which motion is being described.
Speed
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A measure of how fast an object is moving.
Average velocity
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The time-average of the velocity function over a specified time-interval.
(See formula below.)
Instantaneous velocity
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The value of the velocity function at a particular instant in time. (See
formula below.)
Gravitational acceleration
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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/s2.
Scalar-valued function
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A function that outputs scalars (regular
numbers). Most common functions that you are probably familiar with are
scalar-valued functions.
Vector-valued function
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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
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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
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This function is the time-derivative of the position function, and
gives the velocity of an object at each point in time.
Acceleration function
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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
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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
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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
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The average velocity for an object with position function x(t) over the
time interval (t0, t1).
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vavg = 
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The instantaneous velocity at time t for an object with position function
x(t).
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v(t) =  
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