Students in a school rocketry club have prepared a two-stage rocket. The rocket has two small engines. The first will fire for a time, getting the rocket up partway. Then the firststage engine drops off, revealing a second engine. After a little time, that engine will fire and take the rocket up even higher.
The rocket starts firing its engines at a time $t=0$. From that instant, it begins to move upward with a constant acceleration. This continues until time $t_{1} .$ The rocket drops the first stage and continues upward briefly until time $t_{2}$, at which point the second stage begins to fire and the rocket again accelerates upward, this time with a larger (but again constant) acceleration. Sometime during this second period of acceleration, our recording apparatus stops.
Sketch qualitatively accurate (i.e., we don't care about the values but we do care about the shape) graphs of the height of the rocket, $y$, its velocity, $v_{y}$, its acceleration, $a_{v}$, the force on the rocket that results from the firing of the engine, $\vec{F}_{y}$, and the net force on the rocket, $\vec{F}_{v}^{\text {net }}$. Take the positive direction as upward. Be sure to note times $t=0, t_{1}$, and $t_{2}$ on the time axes of your graphs.