in a car race, car A takes a tym t sec less than the car B and passes the finishing part with a velocity v more than that of the car B .if the cars start from rest and travel with constant accleration A1 and A2 respectively. show that V = T * root over of A1* A2.

Car Time Velocity Acceleration
A T1 v1 A1
B T2 v2 A2

It is given that :
T1 +T = T2
v1 = v2 + v

Now using equation of motion :
s1=u1T1+12A1T12s=12A1T12   ...(1)s2=u2T2+12A2T22s=12A2T22   ...(2)From equation (1) and (2)12A1T12 =12A2T22T2T1=A1A2T1+TT1=A1A2   1+TT1=A1A2   ...(3)v1=u1+A1T1 = A1T1 ...(4)v2=u2+A2T2=A2T2   ...(5)v12=u12+2A1s=2A1sv22=u22+2A2s=2A2sv12v22=2A1s2A2sv1v2=A1A2v2+vv2=A1A21+vv2=A1A2   ...(6)From equation (3) and (6), we getvv2=TT1vA2T2=TT1  (from eq.(5))v=TA2T2T1=TA2A1A2v=TA1A2

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