Ask iit jee aieee pet cbse icse state board community Discussion Response Post to: Guys BReak ur head with these three ultimate problems...2nd one is very tough
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waterdemon (3810)

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Hello Vichu_487 ,

Q.3)

As per the given problem , the initial velocity V1 of Car A
is greater than velocoty V2 of Car B. Car A is Behind Car
B at a distance "L"

To Prevent the collision , atleast the velocity of Car A be
reduced to V2.

Let Car A Take time T ot reduce its speed from V1 to V2

In the same time car B moves distance say "x"

Using the formula,

V2 = U2 + 2aS

We have :

V22 = V12 - 2a(L+x)

Where "a" is the retardation.

Therefore ,

(L+x) = (V12 - V22)/2a ( Equation 1 )

Further using V = U + aT , We have :

V2 = V1 - aT

T = (V1-V2)/a  .........(Equation 2 )

During this inteval the distance "x" travelled by the Car B is given by :

x = V2T = V2(V1-V2)/a (Equation 3 )

Substituting the value of "x" from equation.(3) in Eq.(1)

L + V2(V1-V2)/a = (V12-V22)
/2a

Solve the above part we will get :

L = (V1-V2)2/2a

To Prevent the collision , "L" should be greater than the above value :

Therefore ,

L > (V1-V2)2/2a

2aL > (V1-V2)2

And hence the answer ...

(V1-V2) < (2aL)


Hope you find it useful.

plZ rate me if useful.

Cheers!!!!!!!!!@@@!!!!!!!!!



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