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Standard XIII

Physics

Relative Velocity

Two cars and ...

Question

Two cars and are travelling in the same direction with velocities $v_{1}$ and $v_{2}$ $(v_{1}$ > $v_{2})$ . When the car A is at a distance d ahead of the car B, the driver of the car A applied the brake producing a uniform retardation a There will be no collision when

d < \frac{(v_{1} - v_{2})^{2}}{2 a}

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d < \frac{(v_{1}^{2} - v_{2}^{2})^{2}}{2 a}

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d > \frac{(v_{1} - v_{2})^{2}}{2 a}

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d > \frac{(v_{1}^{2} - v_{2}^{2})^{2}}{2 a}

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Solution

The correct option is C $d > \frac{(v_{1} - v_{2})^{2}}{2 a}$
Initial relative velocity = $v_{1} - v_{2}$ , Final relative velocity = 0
From $v^{2} = u^{2} - 2 a s \Rightarrow 0 = (v_{1} - v_{2})^{2} - 2 \times a \times s$
$\Rightarrow$ $s = \frac{(v_{1} - v_{2})^{2}}{2 a}$
If the distance between two cars is 's' then collision will take place. To avoid collision $d > s$ $∴$ $d > \frac{(v_{1} - v_{2})^{2}}{2 a}$
where d = actual initial distance between two cars.

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