Answer
(a) The shortest time to reach Mach 4 without graying out is 33.8 seconds.
(b) The plane would travel 22.4 km.
Work Step by Step
(a) Let's assume the pilot is accelerating at 4g.
$t = \frac{v-v_0}{a} = \frac{4\times 331~m/s - 0}{4g}$
$t = \frac{331~m/s}{9.80~m/s^2} = 33.8~s$
The shortest time to reach Mach 4 without graying out is 33.8 seconds.
(b) $x = \frac{1}{2}at^2$
$x = \frac{1}{2}(4)(9.80~m/s^2)(33.8~s)^2$
$x = 22,400~m = 22.4~km$
The plane would travel 22.4 km.
