Sketch of energy - height graph

[songoku]

Homework Statement

A firework rocket is fired vertically upwards from the ground. It accelerates uniformly from rest with an acceleration of 8.0 ms⁻² for 5.0 s after which time the fuel of the rocket has all been used. Sketch graphs to show how the gravitational potential energy and the kinetic energy of the rocket varies as it moves from the ground to its maximum height. (Ignore air resistance and assume the mass of the rocket does not change)

Homework Equations

PE = mgh
KE = 1/2 mv²

The Attempt at a Solution

x-axis = height
y-axis = energy

For potential energy, the graph will be straight line starting from origin and has positive gradient.

For kinetic energy, the graph will be straight line with positive gradient until it reaches 100 m (I have calculated the distance traveled for 5 s; until the fuel is out) and then the graph will go down, also straight line with negative gradient (negative gradient > positive gradient) until the graph is back to x-axis.

My answer for potential energy is the same as the answer key, but for the kinetic energy it is not the same. The key answer shows that the graph is straight line starting from certain value of y-axis (there is initial kinetic energy) with negative gradient until it touches x-axis.

I don't understand the answer key. Why is there initial kinetic energy? It should be zero because the rocket starts from rest. And also why the kinetic energy is always decreasing? The rocket accelerates for first 5 s so the kinetic energy should increase, even with respect to height. The kinetic energy will decrease when the fuel is out because of gravity.

Is the answer key wrong or something wrong with my analysis?

I am also wondering about the conservation of energy. The graph from answer key shows that the mechanical energy is constant because the kinetic energy decreases as the potential energy increases. Both graphs have the same gradients. As for my answer, both energies increase at first and then potential energy keep increasing while kinetic energy decreases when the fuel is out. I think for my case the energy from the fuel is converted to potential and kinetic energy so the energy is still conserved. Am I right?

Thanks

 

[mfb]

I agree with your results.
Maybe the answer key started right after the rocket stopped firing? Does this fit to its value for the "initial" kinetic energy?

 

[songoku]

I agree with your results.
Maybe the answer key started right after the rocket stopped firing? Does this fit to its value for the "initial" kinetic energy?

The answer key does not give the value, only rough sketch.

Thanks a lot for your help :)