Define displacement of a particle in linear motion. Does it depend upon the origin?

Displacement ##bard## is the vector difference between the initial and final positions or ##bard = x_f - x_i##

The displacement of a particle in linear motion, say along the x axis is the difference in its initial and final positions. Another way you an define displacement as the difference between the final x coordinate and the initial x coordinate of the particle.

## bard = x_f - x_i##

Examples:

(a) If a particle starts from ##x_i = 3 ## and moves to the right to ## x_f## = 13, then ##bard## is 10 units to the right or + 10 units.

(b) On the other hand, if it starts at ##x_i = 3## units and moves to the left, passes the origin and stops at ##x_f ## = - 5 units, then ##bard## = -5 - 3 = - 8 units or the displacement is 8 units to the left.

(c) If a particle starts at ##x_i = 3## units, passes the origin and goes left to x = -5 and then turns around, goes right again and finally stops at ##x_f## = 10 units, then the displacement ##bard = x_f - x_i = 10 - 3 = 7## units