Chapter 3, Problem 1CQ

Can the magnitude of the displacement vector be more than the distance travelled? Less than the distance travelled? Explain.

To determine

Whether displacement vector is greater or lesser than the distance traveled.

Answer to Problem 1CQ

The magnitude of displacement vector can never be greater than the distance traveled.

Explanation of Solution

Displacement is the shortest distance between initial and final point. Hence, it should be a straight line connecting between them. Distance is the total path traveled by the body. So, it will be always greater or equal to the displacement. This can be understood better from the following diagram.

Consider a particle moving from A to B. If the particle moves from A to B in a straight-line path i.e. ACB, then it will be the shortest distance in a particular direction which is nothing but displacement. Instead, if the particle moves from A to B along the path ADB, it will not have any specified direction and also it will be one of the largest path, which is nothing, but the distance traveled.

Conclusion:

Hence, the magnitude of the displacement vector is always less than or equal to the distance traveled.