How to Calculate Displacement

We find the displacement by determining the object’s initial and final position. The displacement formula is given by:

Δx  = x_f − x_i….. (1)

where, 

x_f is the final position, 

x_i is the initial position, and

Δx is the change in the position of the object.

Let’s say, I kept a golf ball on the origin or the 0 points, as shown in diagram A:

(Image will be uploaded soon)

Now, I move the ball by 3 points to the right, as shown in diagram B.

(Image will be uploaded soon)

Since the ball has moved, which means it has made a displacement, as we can see its initial position was 0 at A and the final is 3 metres at point B, so its displacement can be calculated by using equation 1, which is:

 Δx  = x_f − x_i = 3 − 0 = + 3 m, i.e., to the right.

So, the ball made a displacement of 3 meters from A to B.

Now, the ball moves by − 4 points or − 4 m to point C.

(Image will be uploaded soon)

So, the final position now becomes an initial one and final, x_i = − 4  m. So, we can find the displacement AC by using eq (1) as:

Δx  = x_f − x_i = − 4 − (+ 3) = − 7 m, i.e., to the left.

However, we must remember that displacement doesn’t depend on the position of the origin, as we saw in the diagram, it only depends on the difference between the two positions.

Here, 

x₁  = x-coordinate of point A, i.e., the initial position of an object along the x-axis

x₂ = x-coordinate of point B, i.e., the final position of an object along the x-axis

The horizontal distance, i.e., along the x-axis = (x₂ − x₁)

y₁ = y-coordinate of point A, i.e., the initial position of an object along the y-axis

y₂ = y-coordinate of point B, i.e., the final position of an object along the y-axis

The vertical distance, i.e., along the y-axis = (y₂ − y₁)

We know that displacement is the shortest distance between two points; in a two-dimensional system, a distance formula can be used to find the shortest distance between two points, i.e., P (x₁, y₁) and Q (x₂, y₂), which is given as:

S=(x2−x1)2+(y2−y1)2−−−−−−−−−−−−−−−−−−√�=(�2−�1)2+(�2−�1)2

If an object is moving with constant velocity, then

Displacement = velocity x time

If an object is moving with constant acceleration, then the equation of third law of motion is used to find displacement: 

S = ut + ½ at²

S=v2−u22a�=�2−�22�

where v = final velocity, u = Initial velocity, s = displacement, and a = acceleration.