In which of the following cases of motions, the distance moved and the magnitude of displacement are equal? (A) If the car is moving on a straight road (B) If the car is moving in a circular path (C) The pendulum is moving to and fro (D) The earth is revolving around the Sun
Hint The displacement is the shortest straight- line path between the initial and final positions. However, the distance is the length of the actual path taken by a body while going from the initial to the final positions.
Complete Step-by-step solution The displacement covered by a body when going from an initial position to the final position is the length of the shortest straight- line path joining the two points. However, the distance covered by the body will be the length of the actual path taken by the body when going from the initial to the final position. When the motion of the body is only in one particular direction, then the path covered by the body to go from an initial to the final position has to be in a straight line since motion is only in one direction. Therefore, the magnitude of the displacement and distance will be the same in this case since the displacement is the length of the straight line joining the two positions as explained above.
Therefore option (A) is the correct answer.
Additional Information 1. The SI unit of displacement and distance are the same i.e. meters. 2. Both distance and displacement needs a reference point to be measured. 3. The dimensions used for both displacement and distance are the same. 4. Both distance and displacement are equal if the motion of the object is in a straight line and in a particular direction.
Note When the motion is in two or three directions, there is always a possibility that the body first covers a certain distance in one direction and then the rest in another direction or even a third direction. The sum of all these lengths will always be greater than the length of the straight- line path between the initial and final positions.