According to the product description, it has built-in acceleration profile
The motor operates smoothly with minimal vibration, even at low speeds, and features built-in acceleration and deceleration control for improved starting and stopping performance.
So unless you can find a way to change the internal acceleration, I don't see how you can achieve acceleration control "on the fly" (whatever that means).
Full travel in 0.5 seconds is on the fast side. Without knowing the mass of the object moving, it is impossible to say whether the motor has sufficient torque. With numbers we can calculate solutions, without numbers it is just guesswork.