Dynamics

Position, velocity, acceleration, speed, motion, eigenfrequency, vibrations.

v(t) = velocity

a(t) = acceleration

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 5t^{2}. After three seconds the position equals 5*3^{2}=45 meters.
The formula for velocity is 2*5t^{1} = 10t. De velocity after three seconds will be 30 m/s.

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 5t

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examples]

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) [

examples]

Acceleration to position