Answer:
Ok, i will suppose the situation that:
The rocket has a constant speed S (So the acceleration of the rocket is equal in magnitude, but opposite in direction, to the gravitational acceleration)
Here we can remember that:
Velocity = distance/time.
Then if the distance is the height of the rocket, we can write this as:
H = velocity*time
h = S*t
This is a linear model that represents the height of the rocket as a function of time.
Case 2:
The rocket is fired with an initial velocity v0, but no acceleration:
In this case the only acceleration acting on the rocket is the gravitatonal acceleration pulling the rocket down, so the acceleration is:
a = -g
To get the velocity as a function of time, we should integrate:
a = -g*t + v0
To get the height as a function of time, we integrate again:
h(t) = (-g/2)*t^2 + v0*t + p0
Where p0 is the initial position of te rocket, but the rocket starts at the ground, so p0 = 0m.
The height as a function of time is:
h(t) = (-g/2)*t^2 + v0*t
This is a quadratic equation.
