A certain model rocket has an engine that will provide a constant upward acceleration for $2$ seconds, and the

rocket will rise to a maximum height of $1000$ meters before returning to the ground. Ignore air friction in this

problem!

$($a$)$ Sketch a velocity time graph for this problem. Identify the slope of any straight lines in your plot, as well

as the times when $(0)$ the engine starts, $(1)$ the engine stops, $(2)$ the fastest upward speed occurs, $(3)$ the

minimum upward speed occurs, $(4)$ the highest point is reached, and $(5)$ the rocket returns to the ground.

$($b$)$ On one of the launch attempts, the engine malfunctions after one second and stops accelerating the rocket

upward. How high does this defective rocket go$?$A certain model rocket has an engine that will provide a constant upward acceleration for $2$ seconds, and the

rocket will rise to a maximum height of $1000$ meters before returning to the ground. Ignore air friction in this

problem!

$($a$)$ Sketch a velocity time graph for this problem. Identify the slope of any straight lines in your plot, as well

as the times when $(0)$ the engine starts, $(1)$ the engine stops, $(2)$ the fastest upward speed occurs, $(3)$ the

minimum upward speed occurs, $(4)$ the highest point is reached, and $(5)$ the rocket returns to the ground.

$($b$)$ On one of the launch attempts, the engine malfunctions after one second and stops accelerating the rocket

upward. How high does this defective rocket go$?$