in a car race, car A takes a tym t sec less than the car B and passes the finishing - Physics - Motion In A Plane

Question

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

Rajendra Kumar · Accepted Answer

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+12A1T12⇒s=12A1T12   
(1)s2=u2T2+12A2T22⇒s=12A2T22   
(2)From equation (1) and (2)12A1T12 =12A2T22⇒T2T1=A1A2⇒T1+TT1=A1A2   ⇒1+TT1=A1A2   
(3)v1=u1+A1T1 = A1T1 
(4)v2=u2+A2T2=A2T2   
(5)v12=u12+2A1s=2A1sv22=u22+2A2s=2A2sv12v22=2A1s2A2s⇒v1v2=A1A2⇒v2+vv2=A1A2⇒1+vv2=A1A2   
(6)From equation (3) and (6), we getvv2=TT1⇒vA2T2=TT1  (from eq
(5))⇒v=TA2T2T1=TA2A1A2⇒v=TA1A2

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

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.