Alan

acceleration is the rate of change of velocity with time, so you differentiate velocity with respect to time: a = dv(t)/dt

If the question is: what is the volume of a cube of side length 12, the answer is 12*12*12 = 1728.

If the question is: given a volume of 12 what is the side length the answer is ³√12 ≈ 2.289

Yes, that's what I assumed.

Think of x as a label on a box.  Inside the box is a number which you have to find by manipulating a balance (the equation).

On the right-hand side is a number equal to 21 with two boxes taken away.  Make this side 21 by adding two boxes to it.  To maintain the balance though, you also have to add 2 boxes to the left-hand side. So you get:

7x = 21

Now you have 7 boxes on the left-hand side, but you only want one, so divide the left-hand side by 7 to be left with just x. Again to keep the balance you also have to divide the right-hand side by 7, and since 21/7 is 3 you are left with:

x = 3.  This is the number in the box!

The following should help:

Note:  Use integration by parts to do the integral I left to you: Let u = t and dv = e^-(1/3)tdt. Then ∫udv=uv-∫vdu

Another ambiguous question, because of the lack of brackets.  Again, making assumptions about what is wanted we have:

This would be easier if you used brackets to clarify what is and isn't a power!  However, I'll make the assumption that the following is what you are looking for:

I agree that "feel" is somewhat subjective; but, in this case, most people would agree on the effect (I've just tried it myself and it's fairly clear-cut) if not the magnitude of it.  To me, that suggests there is an underlying physical mechanism, related to the material being touched.  My further thoughts on this are as follows:

There are two physical requirements for removal of heat from a finger, say, when it touches a solid surface.

The first is that the material in contact with the finger is capable of conducting the heat away. A better conductor will conduct the heat away better, so one up for thermal conductivity.

However, the second requirement is that there be a temperature difference between the material in contact with the finger and the rest of the material. If the local temperature of the solid doesn't rise, the heat will not flow away no matter how good the thermal conductivity. The local material will rise in temperature quicker and hence start to remove heat more quickly if it has a smaller specific heat capacity. One up for specific heat capacity.

Both properties are involved.

I'm tempted to construct a simple mathematical model of the process!

"Question 1 of my last post. I am not sure why it is positive answer from your post."

The field direction is positive, by convention, going from positive to negative, so it must be going away from the positives spread through the sphere.

"That is that i should or shouldnt use signs when using Fe equations in front of proton charge or electron charge? As well i am unsure what is R^3 in your equation"

Use negative sign when it's an electron and positive when a proton.  R is the radius of the sphere (have a look at the sphere drawn just below the graph), given as 7.04fm (7.04 femto metres = 7.04x10^-15m in your question), R^3 is R raised to the power 3 (or R³).