Two cars P and Q start from a point at the same time in a straight line and their positions are represented by xP(t)=at+bt2and xQ(t)=ft-t2 . At what time do the cars have the same velocity?

Position of the car P  at any time  t, is xp(t)=at+bt2vP(t)=dxP(t)dt=a+2bt……….(1) Similarly, for car QxQ(t)=ft-t2vQ(t)=dxQ(t)dt=f-2t…….(2)∵vP(t)=vQ(t)(given) ∴a+2bt=f-2t or, 2t(b+1)=f-a∴t=f-a2(1+b)