# Can Displacement Be Zero: 7 Facts (Read This First)

The displacement is a change in the position of an object with time. The question pop-ups in mind, can displacement be zero if the object is in motion! Then the answer is Yes.

The displacement of an object is zero if the change in position of an object at two different times is zero. That is, the position of the object is found to be stationary. Not only the displacement of an object at rest is zero, but it is also true for rotating objects at a fixed rotational axis or up and down motion at a fixed point.

## When displacement is zero?

The displacement is zero if the change in position with time is zero. There can be positive laps of the distance, but the total displacement sums to be zero.

There are various examples that define the zero displacements of an object or system. If the body moves to a certain distance and then returns back to the same position where it was standing before, then the displacement of an object becomes zero.

The distance is the total length traveled by the object in motion, but the displacement is the change in the position of an object with respect to the initial position. Hence, the total displacement is the difference between the final and the initial position. If the difference between both is zero, then the displacement of an object is zero.

The example of zero displacements can also be the pendulum oscillating at one end fixed to the rigid body on the top. After frequent oscillations, the pendulum will come to rest in its original position. Thus, the net displacement of the pendulum is zero.

## Why displacement can be zero?

The displacement can be zero because there is no change in the position of an object. The initial and the final position of an object remains the same.

If there is no change in the position of the object, that is, if the object remains at rest, or the object in motion returns back to its original location, then the displacement of an object can be zero.

If a person drives from the home to the office, then the displacement is positive, but when he returns back to his home, his total displacement from the initial to the final time becomes zero.

Another example is a bouncing ball; the ball moves high in the upward direction and then returns back to the ground all the time. The ball covers a positive distance on each bounce but remains at the same position. Hence the displacement of the ball is zero.

## How displacement can be zero?

The displacement is a vector quantity. It has a particular direction as well as a magnitude.

Based on the direction of an object moving in the reverse direction, its displacement can be negative also. If a positive and negative displacement of a body is equal in magnitude, then the net displacement of a body is zero.

Any object is thrown vertically upward, the object will accelerate upward and then returns back to the ground by the action of gravitational force on the object. The object returns back to the same position then the displacement of the object becomes zero.

The displacement of an object in a centripetal motion is always zero. This is because the object in a centripetal motion moving along the circular path will return back to its same original point after every revolution around a fixed center of the circle. Thus the displacement of an object in a circular path is zero.

## When displacement can not be zero?

The displacement cannot be zero if the object is displaced from its initial position and does not return back to the initial position by reversing the direction of its motion.

The non zero displacements are achieved when the object in motion does not return back to its initial displacement. In this scenario, the displacement of an object cannot be negative or reversed in any way.

The non zero displacements can’t be obtained for the object in rotational motion at a fixed axis, the bouncing objects at a point, or objects in harmonic motions, or vibrating back and forth. In all these cases, the displacement of the object is zero. In contrast, the non zero displacements can be achieved in the linear, projectile, or rectilinear motion.

The variable position of an object with time is said to have the displacement, and hence the displacement can not be zero in those cases.

## Examples of Zero Displacement

Some examples of zero displacements are as follows:-

Bouncing Ball:- The bouncing ball bounce on the ground, moves upward, and returns back to the same position on the ground and again bounces up in the air and again returns back to the same position, thus making the total displacement of a ball zero.

Particle in a Transverse Wave:- The particle in a transverse wave oscillates up and down in a harmonic motion; hence the net displacement of a particle in a wave is zero.

Vibrating String:- On application of tension on a string, it vibrates in a harmonic motion and comes back to its rest at its original state. Thus, the displacement of a vibrating string is zero.

The Motion of Curtains:- The curtain moving with the blowing winds will move and comes back to its resting position. Thus, the displacement of curtains is zero.

Wave on Water:- The wavy nature of the wave is due to the harmonic motion of the particles present at the surface of the water. Hence, the displacement of the water molecules is zero.

Flapping Wings:– The birds flap their wings each time, thus making the displacement of the wings zero.

Pendulum:- The bob of a pendulum returns back to its position of rest each time, thus making the net displacement zero.

### Problem: A car traveling along the north direction for a distance of 35 km and then take a turn towards the left and travels 10 km. It then again turns left and covers 35 km and travels another 10 km turning left. What is a displacement of a car?

Solution:- The initial displacement of a car is 35 km towards the North. It then turns left and covers 10 km. After that, it takes a left turn and drives 35 km. At this time, the position of a car is perpendicular to the initial position of a car from where it had started, and it is 10 km from the initial location. It again takes a turn and covers 10 km. The same is shown in the below diagram:-

The car reaches its initial location; hence the total displacement of a car is zero.

#### Conclusion

The displacement is a change in position with time and it can be zero if the object returns to its original position or continues to remain at the same location while it is in motion. This is seen in vibrational motion, rotational motion, translational motion, or an object in linear motion returns to its initial position.