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I understand that plugging values is a better way but this is how i did it....
"If two cars want to maintain a time interval of 1 second between each other" think of it this way => distant is given interms of time (1 sec)..ie ...'D' meters / 1 sec (or D m/s) hence velocity to be maintained = distance => substitute D=V or V=D in above equation => we get V^2 - 100V + 900 < 0 ( < sign indicates required condition ..ie..Speed which will not breach the safety barrier ) => on solving this we get (V-90) (V-10) < 0 => thus it is clear that any speed between 10 m/s to 90 m/s is OK but nothing out of this range....Hence answer is 5 m/s
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V= d/t therefore V = d/1 therefore V=D D = (D^2/100) + 9 100D = D^2 + 900 D^2 -100D + 900 D = 10 or 90 Therefore, to meet the specifications of the formula the answer must be between 10 and 90 so the answer must be A.
I have no idea if I did it right, but I did get the right answer!
The biggest issue is the awkward wording of the question. It would be better if it was clarified that breach meant go in excess of as opposed to break. Since you can in theory breach it by going to close or too far. Since Only B and E work out to be exact it should be reworded as such that going over the amount is clear that its incorrect.