Mayavi and Spyder

 Mayavi and Spyder don't seem to get along. I am doing some mlab.points3D plotting. The Mayavi Scene keeps hanging. It works sometimes, but doesn't most of the time. But, if I run the same script from IDLE, it works fine. I'm yet to figure out what's going on.

Reexamining constant acceleration motion in high school physics

Consider the problem of motion in a straight line with constant acceleration. A complete description of the motion involves 5 quantities: the initial velocity ($u$), the time elapsed ($t$), the displacement ($s$), the final velocity ($v$), and the acceleration ($a$). These quantities are, of course, not independent of one another - they are related via physical equations and knowing some can let us know others. So, an important question is: how many of these quantities do we need to know in order to know everything about the motion?

It turns out, we need to know 3 of the 5 quantities. For instance, if we know the initial velocity, the acceleration, and the time elapsed, then we can find the both the final velocity and the displacement. We do so by using the following two equations of motion:
(i)    $v-u=at$
(ii)    $s=ut+{1/2}at^2$

Both the above equations arise from how we define acceleration and velocity. Acceleration, being the rate of change of velocity gives (i) and velocity, being the rate of change of displacement, gives (ii). Getting to (i) is straight forward for constant acceleration since finding the average acceleration is enough. But, getting to (ii) requires integration. So, while introducing it to high school students, the area-under-the-graph approach is usually used instead (which is just a geometric representation of integration).

All in all, these 2 relations are all we have in this problem. But, what about another equation that many people are used to seeing in high school textbooks:
(iii)    $2as=v^2-u^2$

Well, this equation can be derived from (i) and (ii). If we take $t={{v-u}/a}$ from (i) and plug it into (ii), then after a bit of algebra, (iii) is exactly what you get. Similarly, if we take $a={v-u}/t$ from (i) and plug it into (ii), we arrive at another relation:
(iv)    $s=ut+{1/2}(v-u)t$

This relation is in fact what we come across directly if we proceed by the area-under-the-graph approach from the velocity-time graph. Lastly, if we take $u=v-at$ from (i) and plug it into (ii), we get yet another equation:
(v)     $s=vt-{1/2}at^2$

So, we find that equations (iii), (iv), and (v) can be derived from original 2 equations, (i) and (ii). Rather, starting from any 2 of these equations, we can arrive at the rest. Thus, there are only 2 unique equations in this problem. Mathematically, this implies that we can solve for 2 unknowns. This means that, if 3 of the 5 quantities are known to us, the other 2 quantities can be found from the equations. Therefore, 3 is the minimum number of quantities we need to specify in order to uniquely define a constant acceleration motion along a straight line.

Also, an interesting thing to note is that each of the equations mentioned involve 4 of the 5 quantities. There are $^5C_4=5$ ways to select 4 quantities out of 5. So, it makes sense that there 5 equations. Question: why are there 4 quantities per equation?

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