As the rocket cart speeds up, the velocity changes with time which causes the rocket cart to accelerate.
Acceleration is the change in velocity per change in time of motion.
When an object accelerates upwards, the velocity of the object is changing with time.
In addition, speed describes the magnitude of the given velocity. If the speed of an object change with direction, then the velocity of the object is changing.
Since the rocket cart is speeding up, the speed is changing with time and the velocity will be changing as well. This will result in increase of the cart's  acceleration.
Thus, as the rocket cart speeds up, the velocity changes with time which causes the rocket cart to accelerate.
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