2 particles ar moving with constant speed v such that they are always at a constant distance d apart and their velocities are always equal and opposite. After what time they return to their initial positions?
d is diameter of circle :)
C = pi d
t = pi d/v
To find the time it takes for the two particles to return to their initial positions, we can start by defining the problem.
Let's assume that the initial position of one particle is at reference point A, and the initial position of the other particle is at reference point B. The distance between the two particles is d.
Since the velocities of the two particles are equal and opposite, their relative velocity is equal to twice the speed v. This relative velocity will always be directed from B to A.
To find the time it takes for the particles to return to their initial positions, we need to consider their relative movement. We can imagine that the particle at A is stationary, and the particle at B is moving with a velocity of 2v towards A.
The time it takes for the particle at B to reach A is given by the equation:
time = distance / velocity
In this case, the distance is d, and the velocity is 2v. Therefore:
time = d / (2v)
However, this time only represents half of the total time it takes for both particles to return to their initial positions. Since both particles move towards each other, we need to multiply this time by 2:
total time = 2 * time = 2 * (d / (2v)) = d / v
So, after a time of d / v, the two particles will return to their initial positions.