in a carrace car a takes 4z less than car b at the finish and passes the finishing point with a velocity v more thsn car b
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For A
acceleration=a1
total time=t'-t
final velocity=u+v
For B
acceleration=a2
total time=t'
final velocity=u
s=(1/2)a1(t'-t)^2=(1/2)a2(t')^2
therfor
1)(1-t/t')=(a2/a1)^(1/2)
also
(u+v)^2=2a1s
(u)^2=2a2s
dividing both we get
2)(1+v/u)=(a1/a2)^(1/2)
but u=a2t'
so substitute this value in 2 and put value of t' from 1
therefore we get
v=t(a1a2)^(1/2)
v=t root of a1 a2
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