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Standard XII

Physics

Uniform and Non Uniform

The driver of...

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

s \leq \frac{v^{2}}{2 a}

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S \leq \frac{u^{2}}{2 a}

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S \leq \frac{(u - v)^{2}}{2 a}

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S \geq \frac{(u - v)^{2}}{2 a}

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Solution

The correct option is D $S \geq \frac{(u - v)^{2}}{2 a}$
• As mentioned,
The speed of train A = $v_{1}$
The speed of train B = $v_{2}$
• 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 - 2 $α$ s
v = 0
u = $v_{1} - v_{2}$
0² = u² - 2 $α$ s
- u² = -2αs
- $(v_{1} - v_{2}) ²$ = - 2αs ( - α = retardation )
$\frac{(v_{1} - v_{2})^{2}}{2 α}$ = s
OR
s = $\frac{(v_{1} - v_{2}) ²}{2 α}$
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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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

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