Question

Suppose our school is \[1{\text{ }}km\] away from our house, and we go to school in the morning, and in the afternoon we come back. Then, the total displacement for the entire trip is ………

Answer 1

Hint: The definition of displacement has to be known for a motion of a particle. Displacement is calculated by evaluating the change in position of the particle. For determining the displacement only the initial position and the final position are needed. The distance of the whole path crossed by the particle is not necessary.

Complete answer:
When a particle travels some path with motion in a certain time, the displacement of the particle is defined by the difference between the initial and final position.
For a circle, if a particle starts its journey from a certain point and comes back to that particular point, the displacement is zero due to that there is no difference between the initial position and the final position i.e the difference is zero.
In the above problem, the total path distance i.e the distance between the school and the house is given \[1{\text{ }}km\]. The students start their journey from the house. Let us consider, the house is the initial position of them. After reaching school in the morning, they come back to the house. That means now the final position also becomes the house.
Hence, we can say the initial and the final position are the same for their entire trip. Therefore, the displacement is zero because of the zero difference between the initial and final positions.
The total displacement for the entire trip is Zero.

Note: There is a huge difference between the distance and the displacement.
The distance is the length of the total path that is crossed by the particle in its motion. For the above problem, the students cover the total $1 + 1 = 2km$ path. Hence, the distance will be $2km$. It is a scalar quantity and can not be zero.
The displacement is the shortest distance between the initial and final positions of the particle. It is a vector quantity and can be zero.