Answer:
[tex]t=4s[/tex]
Explanation:
We want to write the equation of displacement (vertical in this case) for accelerated motion, which is [tex]y=y_0+v_yt+\frac{a_yt^2}{2}[/tex]. If we take the upward direction as positive, assume it starts from rest and from the ground, and [tex]a_y=24m/s^2[/tex] (the units are wrong in the text, if accelerates at that magnitude, it's an acceleration, in particular in [tex]m/s^2[/tex]), then we have [tex]y=(12m/s^2)t^2[/tex].
We want to know the time when [tex]y=192m[/tex], so we need to solve [tex]192m=(12m/s^2)t^2[/tex], for which we have:
[tex]t=\sqrt{\frac{192m}{12m/s^2}}=4s[/tex]
This means it takes 4 seconds for a rocket accelerating at [tex]24m/s^2[/tex] to reach a height of 192m.
