Does a spacecraft accelerating in space continue accelerating even after a burst of thrust or does it slow down?

Question

Can someone explain in PHY101 terms:

Q1. Does a spacecraft accelerating in space continue accelerating even after a burst of thrust or does it slow down?

Maybe a more generic question is, "why Newtons equations explain why higher derivatives (of motion) are not maintained in space?"

I know almost nothing about Physics and have forgotton almost all of Calculus but I truely wish to understand so please please don't just say it is obvious.

Key Thoughts:

1. Is this a simple Calculus derivative thing?

2. We're not talk about in an inertial reference frame.

3. We're talking about the observer is on Earth looking through a telescope at a space craft accelerating in space. It is from this observer.

Bonus Question:

Q2. Is the answer to Q1 true even in the world of Quantum Mechanics?

Answer 1

Thrust exerts a force on the spacecraft, so, for any non-zero thrust, the spacecraft has a non zero acceleration (related to the thrust by Newton's Laws.)

When the thrust is zero, the acceleration is zero, so the spacecraft continues moving with whatever velocity it has.

Answer 2

Forces sum -- $\sum{F}=ma$. If your only force is a thrust, and the thrust ceases, you will stop accelerating the instant the thrust ceases, but you will not slow down. Slowing down requires a negative acceleration, rather than zero acceleration.

In an inertial frame this process is simple. In a non-inertial frame, such as an observer on the ground watching the spacecraft move, you will need to use the equations of motion for that particular rotating frame. In a rotating frame, you will see an acceleration of $\frac{v^2}{r}$ to account for the centripital effects, and $\Omega \times v$ for Coreolis effects. These are not attributed in any way to the thrust. They are purely artifacts of the fact that you are observing the spacecraft in a rotating frame.

As for QM, don't worry about it. The short answer is "yes, it still works," because we still fly spacraft, despite believing in quantum mechanics. However, if you really want an answer to that question, it's going to have to go into a lot more mathematical rigor, and lots of calculus. And in the end, the result will be the same. Newton's laws were developed because they did a very good job of predicting how things moved in the sky. The fact that we discovered QM didn't change that Newton's laws were still very good at predicting how things moved in the sky. QM just adds a bunch of statisticla expectations and Hilbert spaces and interpretations that cloud the issue.