A) \[d<\frac{{{({{v}_{1}}-{{v}_{2}})}^{2}}}{2a}\]
B) \[d<\frac{v_{1}^{2}-v_{2}^{2}}{2a}\]
C) \[d>\frac{{{({{v}_{1}}-{{v}_{2}})}^{2}}}{2a}\]
D) \[d>\frac{v_{1}^{2}-v_{2}^{2}}{2a}\]
Correct Answer: C
Solution :
Initial relative velocity\[={{v}_{1}}-{{v}_{2}}\], Final relative velocity \[=0\] From \[{{v}^{2}}={{u}^{2}}-2as\]Þ\[0={{({{v}_{1}}-{{v}_{2}})}^{2}}-2\times a\times s\] Þ \[s=\frac{{{({{v}_{1}}-{{v}_{2}})}^{2}}}{2a}\] If the distance between two cars is 's' then collision will take place. To avoid collision \[d>s\] \[\therefore \]\[d>\frac{{{({{v}_{1}}-{{v}_{2}})}^{2}}}{2a}\] where \[d=\] actual initial distance between two cars.
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