What is the condition for distance travelled by a body is equal to displacement

When the body travels the shortest distance or travels in a straight line, it's distance becomes equal to displacement.

Explanation:

Distance is the actual path covered while displacement is the shortest path or distance covered.

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when two balls of the different masses are dropped from equal height, they reach the ground at the same time .this is because they experience the same acceleration.

the acceleration is independent of mass.

thus when they are dropped they will always maintain the same velocity and travel the same distance (neglect air resistance of course) at the same time.