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
• 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 = v1−v2
0² = u² - 2αs
- u² = -2αs
- (v1−v2)² = - 2αs ( - α = retardation )
(v1−v2)22α = s
OR
s = (v1−v2)²2α
The distance should be more in order to avoid the collision, which proves the above equation.
Hence option D is correct