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What thrust is needed to give a 3.5*10^6 kg rocket carrying 1.8*10^6 Kg of cargo at an acceleration of 3.5m/s2?

acceleration=force/mass

force= 3.5*(3.5E6+1.8E6) N

F = m a

T-(5.3*10^8*9.81) = 5.3*10^8(3.5)
or
T = 5.3*10^8 * (9.81+3.5)

Thats the answer i had but my teacher stated that was incorrect

it depends on what your teacher assumes: is the rocket working on the surface of Earth upward (overcoming gravity), or in free space.

i believe free space. Im just really confused on how to do this

could there be any other answer to this?

free space, go with the answer I posted. On Earth, you have to subtract mg to get net force.

could you show me how you do it for on earth?

just not sure what you mean by subtract mg

I did it for on earth. Bobpursley did it for in space with no gravity.