The idea of a velocity vector comes from classical physics. By representing the position and motion of a single particle using vectors, the equations for motion are simpler and more intuitive. Suppose the position of a particle at time t is given by the position vector s(t) = (s_1(t), s_2(t), s_3(t)). Then the velocity vector v(t) is the derivative of the position, v = (d s)/(d t) = ((d s_1)/(d t), (d s_2)/(d t), (d s_3)/(d t)).

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