Question

Two particles are moving with constant speed v such that they are at a constant distance d apart and their velocities are always equal and opposite. At what time will they reach to their the initial position

Answer 1

As the two particles moving with constant speeds are always at a constant distance d,they must be at the two ends of diameter of a circular path Each particle will return to its initial position after completing the circular path = 2 Î r=Î d
Time interval=Distancespeed=Î dv

Answer 2

We have,

Velocities of the given particles = v

Distance constant between them = D

By observation, the distance between them = diameter of the circular path.

∴ Radius of the path = D/2

Let time taken by the objects to reach their initial position = t

We know,

v = 2πr/t

⇒ t = 2πr/v

⇒ t = [2π × (D/2)]/v

⇒ t = Dπ/v {Answer}