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1. object at rest will remain at rest unless acted on by an unbalanced force. An object in motion continues in motion with the same speed and in the same direction unless acted upon by an unbalanced force.
2. Acceleration is produced when a force acts on a mass. The greater the mass (of the object being accelerated) the greater the amount of force needed (to accelerate the object).
3. For every action there is an equal and opposite re-action.

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As the car is moving it starts gainin momentum and the impulse is the force from the lever acting on it

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When the cars lever is pulled back it has a great amount of potential Energy and when the lever reaches the bottom the energy has converted in to Kenetic energy

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Newtons third law affects the car because for every action there is an equal and opposite reaction. That means that as the car is rolling that friction is pushing against it with not as much force so the car still moves. But as the car keeps going the forces equal out and the car slows down until it finally stops.

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Newtons second law of motion affects mousetrap car because the more the car weighs the slower it goes. So the less the car weighs the faster it will go due to it having less mass so it doesn't take a significant amount of force to move it.

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The mouse trap car relates to Newtons first law because the car does not move until the force of the mousetrap moves it and then it doesn't stop until it hits something or until gravity finally stops it after a certain amount of distance.