Meeting of A and B

To determine when A and B will meet, we need to analyze their relative motion. A moves with a constant velocity u along the x-axis, while B always has a velocity towards A. B moves with a constant speed v.

Understanding the scenario

Let's consider the situation from A's frame of reference. In this frame, A is stationary, and B is moving towards A with a velocity of v. Since A is stationary, the relative velocity of B with respect to A is v.

Determining the time of meeting

We know that distance = velocity × time. Since B is moving towards A, the distance between them will reduce with time. Let's denote the time of meeting as t.

The distance traveled by B in time t is given by:
Distance = velocity × time = v × t

Since A is moving with a constant velocity u, the distance traveled by A in time t is given by:
Distance = velocity × time = u × t

Since A and B meet at the same point, the distances traveled by both A and B must be equal. Therefore, we can equate the two distances:

u × t = v × t

Solving for time of meeting

To find the value of t, we can cancel out the common factor of t on both sides of the equation:

u = v

Therefore, A and B will meet after a time t = 0, when they are both at the same initial position.

Distance traveled by A and B

Since A and B meet at the same point, the distance traveled by both A and B is the same. In time t = 0, they have not traveled any distance.

Hence, the distance traveled by A and B when they meet is 0.

Conclusion

A and B will meet after a time t = 0, when they are both at the same initial position. The distance traveled by A and B when they meet is 0.