Time is not dependent upon anything. Time is what it is.
However, the amount of time necessary for something to happen IS dependent upon the amount of energy put into it, the amount of mass it is happening to and the distance across which it is happening.
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The dimension of power is (energy / time)= (force x distance) / time= (mass x distance / time2) x distance / time= mass x distance2 / time3= ML2T-3
A dependent variable is what is being measured in the experiment. Such as time, distance, volume, etc.
Momentum. Distance divided by time is speed. Mass times speed is momentum.
The independent variable is one that does not depend on the other variable. A dependent variable "depends" on the other variable. Think about the distance traveled by a car over time. You have two variables in that, time and distance. Now think about which depends on the other. Does time depend on distance? No. Time will keep going even if the car stops. Does distance depend on time? Yes. The more time that goes on, the more distance is traveled. So distance is the dependent variable, because it depends on time. Time is the independent variable because it doesn't depend on distance.
Distance is dependent on time. If there is no time, there is no distance, as distance = velocity * time. As time or speed increases so will distance, therefore, if distance increases, either speed or time must increase. If either speed or time = 0, then distance will equal 0.