Ninety percent of the initial mass of a rocket is in the form of fuel. If the rocket starts from rest and then moves in gravity-free empty space, find its final velocity \(v\) if the speed \(u\) of its exhaust is

(a) \(3.0 \mathrm{~km} / \mathrm{s}\) (typical chemical burning),

(b) \(1000 \mathrm{~km} / \mathrm{s}\),

(c) \(c / 10\), where \(c\) is the speed of light.

(d) If the exhaust velocity is \(3.0 \mathrm{~km} / \mathrm{s}\), for how long can the rocket maintain the acceleration \(a=10 \mathrm{~m} / \mathrm{s}^{2}\) ?