I disagree.
Acceleration can never be constant because of the nature of what it means. To advance in speed at every moment, or to CHANGE in speed at every moment, which means it is not a constant.
Notice how you are ignoring what acceleration is and instead focusing on speed?
Yes, a constant acceleration will result in a change in speed. So what? That doesn't mean that it can't be constant.
Consider a constant speed or constant velocity. That means you are continually changing your position. Does that mean it can't be constant? No.
A constant acceleration means your acceleration is constant. That is your change in speed is constant.
Of course you can slow down but you can never decelerate.
What is the difference?
Are you saying if you try and slow down you drop that speed instantly?
Rocket fuel is part of the mass and that burning mass does reduce the mass of the rocket.
However, the rocket is always at full thrust and that full thrust ensures the ejected burning mass matches the mass of the rocket to atmospheric push, so you're always getting a thrust to mass ratio that keeps the rocket at a constant velocity.
No you aren't.
The thrust the remains the same while the mass changes.
That means the thrust to mass ratio changes.
The only way to accelerate that rocket at full thrust would be to lose some of the rocket with each inch (for the sake of it) it moves vertically.
Such as what it does by burning the fuel.
Dumping the burning mass of fuel will keep the mass of rocket constant.
No it doesn't.
The fuel is being accelerated with the rocket until it is burnt and dumped and thus it constitutes part of the mass of the rocket.
Yes but that energy has to release from the rocket with fuel or as it (in terms of a bottle rocket or whatever).
Why can't it release as burnt fuel?
There's no such thing as throttling back on a rocket engine unless you are doing horizontal flight or water/ground based rocket propulsion.
That depends upon the engine. Lots are capable of throttling down.
Vertical flight requires no throttling down and would be absolutely counterproductive to the rocket flight.
And that is beside the point. The simple fact is you can do that.
The thrust always has to be greater than the mass of the rocket to move it.
Not the mass, the weight.
The thrusting fuel will always be at maximum.
And if this maximum is above the weight guess what? That means it continues to accelerate.