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Newton's second law:
A body experiencing a force F experiences an acceleration a related to F by F = ma, where m is the mass of the body. Alternatively, force is equal to the time derivative of momentum.
If force = mass x acceleration, then acceleration = force / mass. The problem says the force is constant, but the acceleration is going up. This means the mass must be going down
. As the fuel is burned, the shuttle weighs less and less, so it starts to accelerate more.
Hope that helps. Post any questions.