Two particles are moving at a speed v such that they are always at a constant distance d apart and their velocities are always equal and opposite.at what time they return to their initial positions?
this is tricky. In my opinion, two object moving at the same and opposite direction means that both object traveled from a different point of origin. So if we have these objects stuck together because of the constant d, then i guess neither of the object will make it to the initial position.
in short, both object cannot get to the initial position.
The time should be 2πr/v
The time should be 2πr/v...as both the particles are at a constant distance d...therefore for one particle-
Distance covered =circumference
Velocity =v
Therefore..t=2πr/v
To determine the time at which the particles return to their initial positions, we can use the concept of relative motion. Since the velocities of the particles are always equal and opposite, we can consider one particle as stationary and the other particle moving with a velocity of 2v relative to the stationary particle.
Let's assume that the initial position of the stationary particle is the origin (0,0) on the coordinate plane. The other particle will then start at a distance of d units on the x-axis from the origin.
Now, we need to find the time taken for the moving particle to reach back to the origin. We know that time, distance, and velocity are related by the formula:
time = distance / velocity
In this case, the distance between the moving particle and the origin is d units. Since the velocity of the moving particle relative to the stationary particle is 2v, we can express the time taken as:
time = d / (2v)
Therefore, the time taken for the moving particle to return to the origin is d / (2v).