How can the motion of an object that is already moving change? An object that is already moving can . . .

Suppose you have an object moving at a constant velocity.

Remebmer that the first Newton's law says:

"Every object will remain at rest or in uniform motion in a straight line unless compelled to change its state by the action of an external force"

There are two possible changes to the motion of this object:

1) A change in the velocity: This happens when we have a force that is parallel to the direction of the velocity vector. This means that the acceleration points in the same or opposite direction than the velocity, then we can have an increase in velocity, or a decrease in velocity (if the acceleration is in the opposite direction of the velocity, eventually the direction of the velocity will also change to match the direction of the acceleration).

2) A change in the direction: When we have a force that is not parallel to the velocity direction, this will change the direction of motion.

Suppose an object that is moving in the positive x-axis, and there is a force applied in the positive y-axis. Now the direction of motion will be in between the positive x-axis and the positive y-axis.