A particle is said to move with uniform velocity if it undergoes equal displacements in equal intervals of time, however small these intervals may be.
In this case, the velocity is equal to the displacement vector per unit
time interval and is given by
When a particle moves with uniform
velocity, we always get the same value of from the above equation, irrespective of the values of
t, t'. In order to obtain the formulae for uniform motion in two dimensions, we begin with the formulae for uniform motion in one dimension, which are,
The same formulae can be generalised for uniform motion in two dimensions in the following way
These formulae are applicable only to a point object moving uniformly in a straight line in the given plane.
Similarly, for uniform velocity,
where vx and vy are
the rectangular components of
along X-axis and Y-axis respectively.
The magnitude of , also known
as speed, is given by
We have in equation (4)
Equating coefficients of and on both sides of the above equation, we get the two following equations
Here, each rectangular position coordinate depends on time like the position coordinate of a uniform one dimensional position.
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from the above equation, irrespective of the values of
t, t'. In order to obtain the formulae for uniform motion in two dimensions, we begin with the formulae for uniform motion in one dimension, which are,
and 
on both sides of the above equation, we get the two following equations
