Thread: Find an expressjon for velocity?

In a car race, car A takes a time of t sec less than car B at the finish and passed the finishing point with a velocity v m/s more than the car B. Assuming that the cars start from rest and travel with constant acceleration a1 and a2 respectively which of the following is correct?

A) v = t√(a1/a2)
B) v = t√(a1.a2)
C) v = t /√(a1.a2)
D) v = t√(a2/a1)

Originally Posted by fardeen_gen

In a car race, car A takes a time of t sec less than car B at the finish and passed the finishing point with a velocity v m/s more than the car B. Assuming that the cars start from rest and travel with constant acceleration a1 and a2 respectively which of the following is correct?

A) v = t(a1/a2)
B) v = t(a1.a2)
C) v = t /(a1.a2)
D) v = t(a2/a1)

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)
your FINAL ANSWER WILL BE
v=t(a1a2)^(1/2) thats option B