Displacement in Physics

When you go to school, you cover some distance. Suppose there is a large lake in front of your house. Due to it, you have to take the long green path to reach your school.

By the time you reach the school, you cover a distance equal to the length of the green road; but your displacement is equal to the length of the red line.

Table of contents:

• ● What is displacement
• ● Distance & Displacement
• ● Scalar & vector quantities

Distance is the space or ground covered by an object, when it moves. It is the total path travelled by an object.

Displacement is the difference between the initial and final position of an object that has moved; more specifically, it is the shortest distance between the initial and the final position.

The direction of movement is always involved in displacement. The magnitude of displacement may be positive, negative or zero.

Distance & Displacement of an object

Let an object move
1 - from point A to B eastward by 50 units;
2 - then towards north to point C by 30 units further;
3 - then further towards south-west to initial point A.
So, total distance travelled by the object is
50+30+58.31 = 138.31 units.

After travelling a distance of 138.31 units, the object has gained 0 displacement, or we should say no displacement at the end.

This is because calculation of displacement considers the initial and the final position of an object.

We see that the object moved and covered some distance. But the initial and the final position of the object are the same, so the displacement of the object is zero here.

Distance & Displacement of an athelete

Let us take another example.
An athelete begins to run through a circular path having a radius of 300 meter. When she reaches her initial position, the distance covered will be equal to the circumference of the circular path (2πr).

But even though she had made one complete revolution and travelled a distance of 2πr unit, no displacement happened, as her final position is the same as her initial position.

After completion of half-circle, distance travelled from A to B is 942.48m., while displacement occured from A to B is 600m.(AB being the diameter)

After completion of full-circle, distance covered from A to A is 1885m., while displacement occured from A to A is 0.

Scalar and vector quantities:

✫ A scalar quantity has only one property, magnitude. Distance is a scalar quantity, it has magnitude only.
Other scalar quantities are area, volume, time etc.

✫ A vector quantity has both magnitude and direction. Displacement is a vector quantity, it has magnitude as well as direction.
Other vector quantities are force, momentum, acceleration, weight etc.

Distance is scalar, displacement is vector

✓ Distance is a scalar quantity, and it is always positive.
✓ Displacement is a vector quantity, it may be positive, negative or zero.

Distance is a scalar quantity; it has magnitude only, and no direction. On the other hand, displacement is a vector quantity; it has magnitude, as well as direction.

No displacement, no work

✓If displacement of an object is zero, then no work is done.

W.r.t. motion, direction of a moving object has much importance when calculating displacement, velocity and acceleration.

In physics,
Work = Force × Displacement .

So, if displacement is zero, then work is also zero, which means no work is done. Understanding displacement is a requirement prior to proper understanding of velocity and acceleration.

--- x ---