Position, velocity, acceleration, speed, motion, eigenfrequency, vibrations.
Position, velocity and acceleration
x(t) = position
v(t) = velocity
a(t) = acceleration

v(t) = x'(t)
a(t) = v'(t) = x''(t)

Position to velocity
Velocity is the derivative of position.
Suppose the position (in meters) is equal to 5t, in which t is the time (in seconds). After three seconds the position equals 15 meters. The velocity at this point is 5 m/s; the positions derivative. Since the position is a first order function, the velocity will be constant. Now suppose the position formula is 5t2. After three seconds the position equals 5*32=45 meters. The formula for velocity is 2*5t1 = 10t. De velocity after three seconds will be 30 m/s.
Velocity to position
x(t) = V(t)

Velocity to acceleration
a(t) = v'(t)
Acceleration to velocity
v(t) = A(t)

Position to acceleration
a(t) = x''(t)
Acceleration to position