A particle moves on a straight line, the only force acting on it being a resistance proportional to the velocity. If it started with a velocity of $1,000 \mathrm{ft}$. per sec. and had a velocity of 900 ft. per sec. when it had travelled $1,200 \mathrm{ft}$., calculate to the nearest hundredth of a second the time it took to travel this distance.The answer is written in the form of \(a\times 10^{-2}\). Find the value of \(a\).

Let's think step by step and output the final answer within \boxed{}.
user