Question

Can displacement be zero even if distance is not zero? Give one example to explain your answer.
A. Yes. For example, a car travels from point A to B and then comes back. Suppose AB $= 5\,{\text{m}}$. In this case, distance travelled is $10{\text{m}}$, while the displacement is zero.
B. No. For example, a car travels from point A to B and then comes back. Suppose AB $= 5\,{\text{m}}$. In this case, displacement is $10{\text{m}}$, while the distance travelled is zero.
C. No. For example, a car travels from point A to B and then comes back. Suppose AB $= 5\,{\text{m}}$. In this case, displacement and the distance travelled is zero
D. None of the above.

Answer 1

Recall the definition of distance and displacement. Make a diagram of the example given in the options and calculate the distance and displacement of the car when it goes from point A to B and when it comes back to initial position. And check which of the options matches with it.

Complete answer:
At first let us recall the difference between displacement and distance. Distance is the measure of how much total length a body travels when it goes from one point to another. Displacement is the measure of overall change in position of a body. Such that if a body’s initial and final position is the same, that is change in position is zero then the displacement of the body is zero.So the answer for whether displacement can be zero even if distance is not zero is yes, it can be. For example, let a car travel from point A to B and the distance between them is $5\,{\text{km}}$.

Case 1: When the car travels from A to B.
Distance travelled by the car is $5\,{\text{km}}$ and position of the car changes from A to B so its displacement will be the length between A and B which is $5\,{\text{km}}$

Case 2: When the car travels from A to B and then again travels from B to A.
In this case the total length travelled by the car is twice the length of AB that is, distance travelled by the car is $10\,{\text{km}}$. But the initial position of the car was A and the final position of the car is also A so, there is no change in initial and final position that means displacement will be zero.

Now, observing the options we get option A gives us the correct example which matches with our case 2, that is if a car travels from point A to B and then comes back. In this case, distance travelled is $10{\text{m}}$, while the displacement is zero.

Hence, the correct answer is option A.

Note: Always remember displacement is zero, the distance travelled by a body can be non-zero, but when distance travelled by the body is zero then displacement is also zero. Distance is a scalar quantity which has only magnitude but displacement is a vector quantity which has magnitude and direction.