past paper unit 5 qs

can somebody please help me out in this question the answer is supposed to be C but why?

can somebody please help me out in this question the answer is supposed to be C but why?

There are two forces on the rocket.
1. Propulsion forwards, which is constant.
2. The Earth's gravitational field pulling it backwards.
The propulsion is greater than the gravitational force so the rocket accelerates away from the Earth.

Q.
What happens to the gravitational force as the rocket moves away from the Earth?
So what happens to the resultant forwards force?
What happens to the acceleration forwards?

I'll try my best to answer

Gradient of the velocity time graph is acceleration.
The rocket has weight downwards and thrust upwards. The weight consists of stuff like engine, humans inside, material, FUEL. The rocket's weight would decrease with time since the fuel is used up. Hence the upward resultant force would increase on the rocket. By Newton's second law, this means greater acceleration. Hence the increasing gradient for increasing acceleration.

Not sure what they mean by the universe expanding, I've finished AS Physics on Edexcel only, not A2.

so because the thrust force remains constant and the gravitational force is decreasing the rocket will have a resultant force that causes acceleration right?
But then what is the significance of the question saying that the universe is expanding?? (because the previous question ie 8 and 9 in the same exam paper are about astronomy so shouldn't the statement that the universe is expanding have significance related to astronomy or else why say it? )

so because the thrust force remains constant and the gravitational force is decreasing the rocket will have a resultant force that causes acceleration right?
But then what is the significance of the question saying that the universe is expanding?? (because the previous question ie 8 and 9 in the same exam paper are about astronomy so shouldn't the statement that the universe is expanding have significance related to astronomy or else why say it? )

thanks

Maybe they talk about the universe stuff just to put you off and try to trick you. This is really a mechanics kind of question, not astronomy.

The point is not that the rocket just accelerates, but that the resultant forwards force increases and so the acceleration itself increases. This means the gradient, which represents the acceleration on a velocity time graph, is increasing with time so the line curves upwards. Answer C.
The bit about the expansion is not really important as far as I can see for the purpose of actually answering the question.

The increasing acceleration comes from the resultant force between gravity acting to pull on the rocket and thrust acting against gravity.

F_net = F_thrust - F_{gravity .......eq1}


then
F_net = F_thrust - G(M_rocketM_earth)/d^{2 .......eq2}

We can see that since the mass of the earth can be assumed constant, the only other variables that affect the accelerating force are the mass of the rocket and the distance between the earth and the rocket.

The mass of the rocket will be falling linearly since the thrust is constant so if no other force was acting (i.e. in the absence of gravity), the velocity/time graph would be a constatnt acceleration since the same force is acting on less and less mass falling at a linear rate.

Also the gravitational attraction force is falling at a rate governed by the square of the distance between the earth and the rocket.

So the net force in the forward direction must be increasing which produces an increased acceleration.

At large distances however, gravity has little effect and the constant thrust term becomes dominant, but since the mass of the rocket continues falling it will continue accelerating at a constant rate.

What's niggling me is that 'throwaway' statement about the expanding universe. I cannot help but think it refers to the Hubble constant and the 'open, flat and expanding' universe outcomes for Euclidean space. But then that is going beyond an A-level syllabus.

so if we were to continue expanding the graph it will be a parabola first then continue out as a straight line? thanks