The curved line in the figure represents the trajectory of a particle. Let the particle be at P at time t. The position of p with reference to origin
O is given by . Let the
particle be at Q at time (t + Dt). The position
of Q with reference to P is given by . Applying the law of
triangle of vectors,
The displacement takes place in time
Dt. The average velocity of the particle is given by
The instantaneous velocity is given by
The instantaneous velocity vector is always tangential to the trajectory at the point that locates the particle position.
Next, let us understand the significance of the vector relation,
By assuming = 0, let us understand equation (1)
which changes to,
By applying the law of triangle of vectors to the figure above, we can
see that the position vector at any time t is the vector sum of and the components x (t) and y(t) are given by the following equation.
. Let the
particle be at Q at time (t + Dt). The position
of Q with reference to P is given by 
. Applying the law of
triangle of vectors,
= 0, let us understand equation (1)
which changes to, 
and the components x (t) and y(t) are given by the following equation.
