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Standard XII

Physics

Finding Average Velocity

Two cars 1 ...

Question

Two cars 1 & 2 starting from rest are moving with speeds $V_{1}$ and $V_{2} m / s (V_{1} > V_{2}),$ car 2 is ahead of car '1' by 'S' metres when the driver of car '1' sees car '2'. What minimum retardation should be given to car '1' to avoid collision.

\frac{V_{1} - V_{2}}{S}

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\frac{V_{1} + V_{2}}{S}

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(\frac{V_{1} + V_{2}}{2 S})

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\frac{(V_{1} - V_{2})^{2}}{2 S}

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Solution

The correct option is D $\frac{(V_{1} - V_{2})^{2}}{2 S}$
It the acceleration of can I reaches velocity of car 2 before colliding huy will be saved

Let the deceleration is a , so

$t = \frac{v_{2} - v_{1}}{a}$

After time t , distance will be

$d = v_{2} t - [v_{1} t - \frac{1}{2} \times a t^{2}]$

The maximum value of d possible is s
$d < s$
putting value of t
$\frac{1}{2} \frac{(v_{2} - v_{1})^{2}}{a} < S a > \frac{(v_{1} - v_{2})^{2}}{2 S}$
Hence option (D) is correct

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