A toy rocket, launched from the ground

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A toy rocket, launched from the ground, rises
vertically with an acceleration of 39 m/s^2
for 14 s until its motor stops.

Disregarding any air resistance, what maximum height above the ground will the rocket
achieve?

The acceleration of gravity is
9.8 m/s^2

For the first 14 seconds, it is accelerating upwards at 39 m/s^2, with which one can find its height when the rocket just stops. $y_1=\frac 12 at_1^2$
After $t_1$ (14 s), it going into an accelerated motion with -9.8 m/s^2. Use $v_f^2-v_i^2=-2gy_2$, one can find how much additional height it can reach. Here $v_f=0$, $v_i=at_1$.
Total height is $y_1+y_2$.