Introduction:
In this scenario, we have two bodies A and B starting from the same point and moving in the same direction. Body A is accelerating uniformly with an acceleration (a), while body B is moving with a constant velocity (v). We need to determine the time (t) it takes for the two bodies to meet.

Analysis:
To solve this problem, we can consider the motion of the two bodies separately and equate their positions when they meet. Let's analyze the motion of each body individually.

Motion of Body A:
Since body A is moving with a uniform acceleration, we can use the equation of motion to determine its position at any given time. The equation of motion for a body starting from rest with a uniform acceleration is given by:

s = ut + 0.5at^2

where s is the displacement, u is the initial velocity, a is the acceleration, and t is the time.

In this case, the initial velocity of body A is zero. Therefore, the equation simplifies to:

s_a = 0.5at^2

Motion of Body B:
Body B is moving with a constant velocity (v). The equation for the displacement of a body moving with constant velocity is given by:

s = vt

where s is the displacement, v is the velocity, and t is the time.

In this case, the displacement of body B is the same as the displacement of body A when they meet. Therefore, we can equate the equations of motion for body A and body B:

0.5at^2 = vt

Solving for t:
To solve for t, we can rearrange the equation:

0.5at^2 - vt = 0

We can factor out t:

t(0.5at - v) = 0

Since t cannot be zero (as the bodies need time to meet), we can ignore the first factor. Therefore, we are left with:

0.5at - v = 0

Simplifying the equation:

0.5at = v

t = 2v/a

Conclusion:
The time (t) it takes for bodies A and B to meet is given by the equation t = 2v/a. This equation is obtained by equating the displacements of the two bodies when they meet.

2U/a