At the initial moment three points A,B and C are on a horizontal straight line at equal distances from one another. Point A begins to move vertically upward with a constant velocity v and point C vertically downward without any initial velocity at a constant acceleration a.How should point B move vertically for all the three points to constantly be on one straight line? The points begin to move simultaneously.
please help me out quick.

Sorry bro but I think the distance between the points is required because the answer depends on it.

HINT 

Take B on the origin and A at (-d,0) and C at (d,0) now position of A after time t is (-d,vt) and that of C is (d,at²/2) now from these points write eqn of line in two point form and put x = 0 to obtain a relation between y co ordinate of B and the rest of parameters.

• Simplify the eqn and compare to the standard eqn for distance s = ut + at² /2 to obtain the initial velocity and accn.

NOTE : The solution is in general for the point except the bullet because in that point the acceleration has been assumed to be constant otherwise problem becomes too complex.