and the initial velocity is 0, would the rocket move at all? Or would gravity affect the rocket, and make it stay in place?
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Yes, it would accelerate upwards at 9.8 m/s^2. The upward acceleration already accounts for the force of the earth pulling down on it. Think about it, if you're not accelerating at all, so 0 m/s^2, so anything greater than that would mean you are moving.
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Unless the rocket was falling.
If you treat down as the "negative" direction (which is usually what you will do), earths acceleration is -9.8.
If it was 9.8 m/s^2, that would mean that earths acceleration was causing it to speed up, which would mean that it was falling.
If you treat down as the "negative" direction (which is usually what you will do), earths acceleration is -9.8.
If it was 9.8 m/s^2, that would mean that earths acceleration was causing it to speed up, which would mean that it was falling.
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Earth's gravitational field is 9.8 meters a second. The rocket would stand in place.