A particle is moving with constant acceleration from A to B in a straight line AB.  If U and V are the velocities of particle at A and B respectively, then its velocity of particle at the midpoint C will be

let c be the mid point of AB, let velocity at c be x from A to C; initial velocity =u; final velocity =x; distance =d2;acceleration =a substitute in v2=u2+2as---(1) X2  =   U2  + 2a⋅d2          → --     (2) from A to B; initial velocity =u; final velocity =v; distance =d;acceleration =a substitute in equation (1)  v2=u2+2ad ⇒ad= v2-u22---(3) substitute equation (3) in (2) X2  =   U2  + v2-u22 X= v2+u22=velocity of the particle at mid point of AB