Two cars A and B start from a point at the same time in a straight line and their positions are represented by R _ A ( t )= at + bt ^2 and R _ B ( t )=x t - t ^2 . At what time do the cars have same velocity?

Step-by-step solution

Velocity of car A and B: aligned V _ A & = d ( R _ A ) dt & = a +2 bt V _ B & = d ( R _ B ) dt & = x -2 t aligned So, time at which cars have same velocity is array ll & V_A=V_B & a+2 b t=x-2 t & t= x-a 2(b+1) array