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# How are acceleration and force related?

If you have a miniature toy car or even a smooth hard ball that can roll on a smooth level surface you can explore the effects of force on motion. When the toy car or ball is motionless, give it a gentle tap with your finger. Note how it moves. Now, while it is moving give it a second, then a third or even a fourth gentle tap. What happened?

You saw that when the toy car was at rest and a force was exerted on it, it started to move in the direction of the force. When a force was applied in the direction of its motion, it sped up. Each additional tap caused it to speed up more. What do you think would happen if you were able to exert a constant force on it while it was moving? It’s difficult to do, but try it.

You can conclude from this exercise that a force applied in the direction of motion causes it to speed up, or accelerate in the direction of the force. If the direction of motion is called the positive direction, then both the force and acceleration would also be positive.

Now start the toy car moving and give it a gentle tap in the direction opposite its motion. Don’t tap it so hard that it stops or changes direction. See if you can tap it two or three times, again without stopping the car. What did you observe?

You should be able to conclude that a force applied in the direction opposite its motion causes it to slow down, or accelerate in the direction of the force. If you had defined the direction of motion as positive, then the force and acceleration would both be negative.

What happens when no force is applied? You saw in the beginning that when the toy car started at rest it remained at rest until you exerted a force on it. What happened while it was moving? It probably slowed down some, with the amount depending on the condition of the toy car and the hardness of the surface. But, the amount it slowed was certainly much less than it was when you exerted a force in the opposite direction.

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