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However, how are the Force and Velocity independent? Doesn't the Force applied affect the Velocity of the object?

For example, let's say you want to lift a 19.62N (2kg*9.81m/s^2) object upwards 1 meter in 1 second. The way I see the problem solved online is that you would need 19.62W = (19.62N*1m/s). However, with this applied Force the object is in equilibrium (and not moving or moving at an arbitrary constant velocity), so the work and power would be zero.

I must have something wrong here. Thanks.