TITLE: Why current of a battery drops continuously in high currents?
QUESTION [1 upvotes]: I have asked this question on EE SE but could not get a satisfactory enough answer.
I have shorted an AA battery through an ammeter. Inititially, the current reading on ammeter was around 0.9 amperes but it quickly and stedily decreased in time over a period of 10-15 seconds.
I thought that the reason for the steady drop in current is due to a steady drop in voltage when I was shorting the battery. I have reached this conclusion because after breaking the short, I have measured the voltage of the battery and observed that the voltage is "replenishing" steadily at a rate of approximately 2-3mV/sec.
So I am wondering why did I observe such behavior? Why does the voltage over the battery drops steadily on high currents? Also, why does the battery's voltage replenish after breaking the short? What goes on behind the scenes?

REPLY [1 votes]: I thought that the reason for the steady drop in current is due to a
  steady drop in voltage when I was shorting the battery.

When you 'short' the battery with the ammeter, the battery voltage becomes effectively zero volts.  This is because an ammeter has very low resistance between its terminals.  You're essentially measuring the short-circuit (zero voltage) current capability of the battery.  You can verify this by placing a voltmeter across the battery terminals in addition to the ammeter.

Inititially, the current reading on ammeter was around 0.9 amperes but
  it quickly and stedily decreased in time over a period of 10-15
  seconds.

It is likely that your battery is not fresh (fully charged).  Looking at the chart below, note that all AA batteries tested supplied 2A into a constant current load for at least 15 minutes.
Thus, a fresh AA battery should be able to initially deliver considerably more than 2A short-circuit current.  Note that the large short-circuit current will heat the battery while rapidly exhausting the reactants within.

Also, why does the battery's voltage replenish after breaking the
  short?

Essentially a duplicate of Why do batteries recover after a load is removed?


TITLE: Please can you explain to my son and me how to solve this factorisation: $(a-b)^2 - 2(a-b)$
QUESTION [2 upvotes]: $(a-b)^2-2(a-b)$
Please explain how to factor this expression.  My son and I are stuck as we don't know how they come to the answer.

REPLY [4 votes]: For more complex equations like this one, it can help to use an intermediate variable. Here we can use $$a-b=X$$
Now we can rewrite the initial equation as follows $$(a-b)^2-2(a-b) = X^2-2X$$
Hopefully you can easily spot that this can be factorised as $$X(X-2)=(a-b)(a-b-2)$$


TITLE: Does Piston moves faster when we accelerate the car?
QUESTION [0 upvotes]: I am learning about car basics. I found that engine is nothing but a system where heat energy is converted into up/down motion of the piston in the cylinder. Finally, this up/down motion is converted into rotary motion by locking the gear teethes against each other.
So, my understanding is that all that motion is available on the flywheel, when we shift gears, the rod connected from flywheel to the wheel changes the distance from the flywheel. This changes displacement and hence torque ( force * displacement) is changed. So, basically, piston is moving at the same speed only, when we accelerate the differential gears changes the speed. Is it correct? Or is it that when we accelerate even the piston starts moving faster? If yes, how is it possible, since the temperature or heat energy is same, we can't increase the temperature inside the cylinder suddenly on pressing the accelerator. Is my understanding correct here? Also, I see that in my car - the engine rpm doesn't keep changing. It changes a bit but not too much like odometer.

REPLY [1 votes]: No. To increase the speed of the car, you do are 2 things: you press the accelerator, and you change gears.
Pressing the accelerator makes the engine turn faster, even when the car is out of gear and stationary. You can see the engine speed on the tachometer, which shows the Revolutions per Minute (RPM) of the engine. This is the number of times the crankshaft rotates per second. Typical figures are between 500 rpm and 7000 rpm. As every cylinder has to go up and down once for each revolution, they obviously move faster as you press the accelerator pedal further down.
You also need gears because an internal combustion engine has very little torque and power at low rpm, while it also cannot turn faster than some maximum speed without self-destructing. Hence, you use low gear at low speed (to have the engine run fast enough so it has enough power at low speed) and you use high gear at high speed (so the engine won't have to turn at excessive rpm). A good driver will choose the correct gear, depending on what they want to do. To accelerate fast, use a lower gear; to use less petrol, use a higher gear.
If the tacho in your car does not change much, that is because you have an automatic gearbox (or even a CVT gearbox), which changes gears to keep the engine running at optimum speed. If you manually select a gear (or if you drive really fast) you'll see the tacho change.
Note that electric cars do not have this problem. Electric motors have maximum torque at zero rpm. Hence, all you need to do is to set the overall gearing so that the car will go at maximum speed at the recommended maximum rpm of the motor. You do not need to worry about having the motor run at speeds that are too low: it can "run" at 0 rpm; this is unlike a petrol engine which would stall.