It is important to identify correctly all the forces acting on an object. It is equally important not to include forces that do not really exist. We have established a number of criteria for identifying forces; the three critical ones are:
A force has an agent. Something tangible and identifiable causes the force.
Forces exist at the point of contact between the agent and the object experiencing the force (except for the few special cases of long-range forces).
Forces exist due to interactions happening now, not due to what happened in the past.
Consider a bowling ball rolling along on a smooth floor. It is very tempting to think that a horizontal “force of motion” keeps it moving in the forward direction. But nothing contacts the ball except the floor. No agent is giving the ball a forward push. According to our definition, then, there is no forward “force of motion” acting on the ball. So what keeps it going? Recall our discussion of the first law: No cause is needed to keep an object moving at constant velocity. It continues to move forward simply because of its inertia.
There’s no “force of motion” or any other forward force on this dart. It continues to move because of inertia.
A related problem occurs if you throw a ball. A pushing force was indeed required to accelerate the ball as it was thrown. But that force disappears the instant the ball loses contact with your hand. The force does not stick with the ball as the ball travels through the air. Once the ball has acquired a velocity, nothing is needed to keep it moving with that velocity.