Before learning to calculate displacement, let us define displacement and learn what is position vector and how to write it.
Definition of Displacement
Displacement is the measurement of the difference between a particle’s initial and final position. It is one of the basic quantities used in kinematics, which is also used to derive velocity and acceleration. Displacement is a vector quantity, which has both a magnitude (size) and a direction. To calculate displacement, you need to subtract the position vector of the initial position from the position vector of the final position. So, before discussing displacement, it is important to understand how a position is denoted using vectors.
What is Position Vector
A position vector gives the position of a particle with respect to the origin of the coordinate system. In our discussion, we will limit ourselves to a system of 3-dimensional Cartesian coordinates. The position vector for a particle at coordinates , .
How to Calculate Displacement
Suppose a particle moves from a point , that has a position vector to a new position with a position vector position vector . Then the displacement vector is given by .
A particle moves from position to . Calculate displacement vector for this motion.
We have and . Therefore, .
How to Calculate Net Displacement
Suppose a particle moves several times. The net displacement is the displacement vector between the particle’s initial position and the final position. The net displacement can also be obtained by vector addition of each of the individual displacement vectors that corresponds to each stage of motion. For example, in the diagram below, the position vector of the point is and the position vector of the point is . Then, the net displacement .
How to Calculate Magnitude of Displacement
As mentioned earlier, displacement is a vector quantity. The magnitude (size) of this vector quantity gives the distance. If the displacement vector , then the magnitude is given by .
In the earlier example, we had a displacement vector of . The magnitude of this vector is .