A body A moves with a uniform acceleration a and zero initial velocity. Another body B, starts from the same point moves in the same direction with a constant velocity v . The two bodies meet after a time t. The value of t is

To find the time $t$ at which the two bodies meet, we can analyze the displacement of each body from their starting point.

Let the starting point be the origin. Both bodies start from the same point at the same time and move in the same direction. When they meet after a time $t$, their displacements from the starting point must be equal.

1. Displacement of Body A:
Body A starts with zero initial velocity ($u_A=0$) and moves with a uniform acceleration $a$.
Using the second equation of motion, the displacement $s_A$ of body A after time $t$ is given by:
$s_A=u_{A}t+\frac{1}{2}a{t}^2$
Since $u_A=0$:
$s_A=\frac{1}{2}a{t}^2$

2. Displacement of Body B:
Body B moves with a constant velocity $v$.
The displacement $s_B$ of body B after time $t$ is:
$s_B=vt$

3. Finding the meeting time $t$:
Since the two bodies meet, their displacements are equal:
$s_A=s_B$
Substitute the expressions for $s_A$ and $s_B$:
$\frac{1}{2}a{t}^2=vt$

Since they meet after starting, we are looking for a non-zero time ($t\ne 0$). We can divide both sides by $t$:
$\frac{1}{2}at=v$

Solving for $t$ gives:
$t=\frac{2v}{a}$

Thus, the two bodies meet after a time $t=2v/a$.