about 830000kg of fuel is burned in 8min.the fuel provides the shuttle w/ a constant newtons 2nd law of motion

Question

explain why the shuttle's acceleration increases during takeoff?

Answer 1

Easy. During the first two minutes, the thrust is constant, but the shutttle is getting lighter every second. The SSMEs are consuming the LH and LOX propellants. The SRBs are burning the solid fuel. With constant thrust, and continuous loss of mass, the rate of acceleration increases every second.

At the two minute mark, the SRBs are just about used up and they are jettisoned. They are no longer producing thrust, but they are empty and are much lighter than they were. The SSMEs are still running and consuming the LH and LOX. The mass of the shuttle is still dropping, but the SSMEs are still running. The rate of acceleration increases because the thrust is contant while the mass is declining.

Answer 2

Two reasons:

1) The shuttle is getting lighter as fuel is expended, so the thrust is working on less mass.

2) In the first second, the thrust is working against a shuttle that is stationary. In the next second, it is applying the same amount of thrust to a shuttle that is already moving, so velocity increases. In the next second, the thrust is pushing a shuttle that is going faster than it was the last second, so velocity increases. Repeat until thrust stops.