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As soon as this object reaches its peak (v = 0) and begins to drop, does the object steadily picks up its speed just as it did when you threw it up? Like does it begin to accelerate at the same rate (downwards) as it did when you throw it upwards?

Because when you throw it up, gravity affects it, but so does your hands?

So the other part i want to get to is, whenever you read problems like "you throw an object up with a speed of....", and you immediately just have gravity in your equation

[tex]\Delta y = \frac{-gt^2}{2} + v_0 t [/tex]

Is that actually wrong? Because when you throw it up, you actually give an acceleration (hence a force?)

Thanks