*I\'ve never taken physics so I\'m lost please explain step by step/ in detail f

Question

*I've never taken physics so I'm lost please explain step by step/ in detail for me to understand it.

A (positively or negatively) charged rod is brought up to the same distance from each set of metal speres as shown in separate situations as shown. The spheres in each pair are initially in contact, but they are then separated while the rod is still in place. Then the rod is removed.

Rank the net charge on each sphere from the most positive to the most negative after the sheres have been separated and the charged rod removed.

Positive 1____2___3___4___5___6___Negative

Or, all spheres have the same charge.

Please explain your reasoning in detail to understand.

Explanation / Answer

I can suggest a couple of ways of getting d). First, write out the equations of motion for both runners, meaning write out expressions for x(t) for each runner. Now, construct the quantity x2(t)-x1(t) where x2 and x1 are the time dependent positions of each runner take d/dt of x2(t)-x1(t) and set that derivative equal to zero; the value of t that satisfies this equation will be the time of maximum separation; substitute that value into x2(t)-x1(t) to find the actual separation second, you could plot x2(t) and x1(t) on the same set of axes and visually determine the time and amount of separation hope this helps note added later...I checked your work and agree with your accelerations; after looking into it a bit more, I think the best way to solve this is graphically (or a combination of graphing and calc) if you plot x1(t)-x2(t), you will see that the maximum occurs around 2.8 s and has a magnitude of around 4.4m this is at a time when the first runner has reached max speed, and the second runner is still accelerating, so we can write the separation function as: x1(t)-x2(t) = 10.64+10.64(t-2) - 1.875 t^2 differentiate this expression and find that d/dt(x1(t)-x2(t))=0 when t=2.83s, so this is the time of max separation; now, substitute this into the x1(t)-x2(t) expression and find the value of the separation (I get 4.45m)

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