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I give you the result of my calculus without the details: The result is : $$\Delta t = \frac{\Delta x}{V_{Max}} + \frac{1}{2}(\frac{V_{Max}}{a} + \frac{a}{j}) + + \frac{1}{2}(\frac{V_{Max}}{d} + \frac{d}{j})$$ where : $\Delta t$ is the total time. $\Delta x$ is the total displacement. $a$ is the maximum acceleration. $d$ is the maximum ...

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In principle you should be able to elevate water to any height in stages, using intermediate reservoirs located at intermediate heights. So if you split it into n stages then the effective water flow rate would decrease by a factor of n but the effective maximum height would increase by a factor of n - exactly what you want. This can certainly be done in ...

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One thing you can do to get it all at once is to attach a resistor of variable resistance $R$ over the load, and calculate the current going through it as a function of $R$. The expression for current will come in the form $\frac{A}{B+R}$ for some $A$ and $B$. Looking at the equivalent expression in the Thevenin equivalent circuit, we see that $A=V_{th}$ and ...

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Without dependent sources, zeroing all the independent sources leaves a resistor network so that the Thevenin resistance can be calculated directly. However, dependent sources typically alter the Thevenin resistance so those can't be zeroed. One technique is to calculate the open circuit voltage and then place a wire across the nodes and calculate the ...

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Presumably each axle is rigidly attached to its gear (no bending or breaking). This means that the torque on the gear is the same as the torque on its axle. So you can ignore the axles and just think about the gears themselves. And in that case, you can just use the torque ratio of the gears themselves.

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