Newton's First Law- An object at rest tends to stay at rest and an object on motion tends to stay in motion unless an external force is applied.
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If all external and opposing forces were eliminated, and you pushed a ball, the ball would never stop and would keep moving in the same direction forever.
In this demonstration, the driver is not wearing a seat belt. The car comes to an abrupt stop and, considering the insignificant amount of friction, the passenger continues in its state of motion. The seat belt would have been that external force that stops the driver.
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