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h3. Definitions of Position and Velocity

If we start knowing the position vs. time x(t), the velocity, v(t) is the derivative of its position, and the derivative of this velocity is the particle's acceleration, a(t). The force is the particle's mass times a(t).

{latex}\begin{large}\[ v = \frac{dx}{dt} \]\[ a = \frac{dv}{dt} = \frac{d^{2}x}{dt^{2}}\]\end{large}{latex}

In fact, as you can see, the velocity and acceleration are defined as derivatives of the position, a fact acknowledged by the phrase "the calculus of motion".  Newton had to invent calculus of one variable to deal with motion\!