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Question

The driver of a train moving with velocity u finds that another train is moving with a velocity v in the same direction on the track at a distance 'S'. If he applies the brakes and produces a retardation 'a' to avoid accident, then

A
sv22a
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B
Su22a
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C
S(uv)22a
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D
S(uv)22a
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Solution

The correct option is D S(uv)22a

• As mentioned,

The speed of train A = v1

The speed of train B = v2

• Train B is moving with a slower speed than Train B and it produces retardation.

So, acceleration of train A = - α

acceleration of train B = 0

Now, by using formula :

v² = u² - 2αs

v = 0

u = v1v2

0² = u² - 2αs

- u² = -2αs

- (v1v2)² = - 2αs ( - α = retardation )

(v1v2)22α = s

OR

s = (v1v2)²2α

The distance should be more in order to avoid the collision, which proves the above equation.

Hence option D is correct


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