Note: Before addressing this part of the problem, I suggest that you figure out exactly how much you should apply as your spuCraft is passing the first belt. There is a help page here on that subject.
Before reaching a belt, you must get the spuCraft to the right speed. This can be complicated. But it can also be very simple.
My suggestion is to make it simple. You do not get any extra points for a smooth flight in Drop. Let gravity do most of the work. Then fire the thrusters at just the right moment.
I would suggest that you sketch plots of position, velocity, and acceleration. Your plots should start at the bridge and continue until it reaches the first belt. At the bridge, the spuCraft should be motionless. By the time it reaches the belt, it has to be moving at the constant speed of the belt. How do you get from one point to the other? Keep it simple! Remember that it’s OK to match the speed of the belt before you get to the belt.