A rocket initialy at rest on the ground lifts off verticaly with a constant acceleration of 2.0 x 10^1 ....

Question

... meters per second squared. How long will it take the rocket to reach an altitude of 9.0 X 10^3 meters?

Answer 1

Use x = 0.5 a * t^2
where x = height = 9000 m
and a = acceleration = 20 m/sec/sec
and t = time

solving for t:

t = SQRT(2x / a) = SQRT(2 * 9000 / 20) = 30 sec

Answer 2

Although you failed to specify it, I'll assume a = 20 m/sec^2 = constant. In which case, starting from zero velocity, we have S = 1/2 at^2; so that t = sqrt(2S/a), the time to climb you are looking for; where a = 20 m/sec^2 and S = 9,000 meters. You can do the math.