Two cars $A$ and $B$ are moving in same direction with velocities $30 m / s$ and $20 m / s$ . When car $A$ is at a distance $d$ behind the car $B$ , the driver of the car $A$ applies brakes producing uniform retardation of $2 m / s^{2}$ . There will be no collision when

d > 125 m

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d > 120 m

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d < 25 m

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d < 125 m

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Solution

The correct option is C $d < 25 m$
Distance required to catch the speed of car B with given retardation can be found using
$v^{2} = u^{2} + 2 a s$
$\Rightarrow 20^{2} = 30^{2} + 2 (- 2) s$
$\Rightarrow 4 s = 30^{2} - 20^{2}$
$\Rightarrow s= 125m $
So the distance sholud be greater than 125 m
$\Rightarrow d > 125 m$
Therefore, A is correct option

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