suggestions_ned

Question: Check out the link flow_diagrams and give a synopsis of what you see there.

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Your solution:

- RESPONSE:

- - The page at URL http://vhcc2.vhcc.edu/dsmith/genInfo/qa_query_etc/ph1/flow_diagrams.htm contains:

- - - Step-by-step instructions for constructing a flow diagram given certain variables, among which each is specified as being either known (i.e., providing the starting point for calculations) or unknown (i.e., being the value whose calculation represents an intermediate and/or final goal of constructing the diagram -- I say ""a[...] goal"" rather than ""the [...] goal"" because the diagram is used to calculate multiple variables, including multiple variables that represent the output of calculations but don't serve as the input for any, and accordingly is not unilinear.)

- - - Illustrations of the progress of the diagram's construction (http://vhcc2.vhcc.edu/dsmith/genInfo/qa_query_etc/ph1/ph1_qu1.gif, [""]/ph1_qu8.gif, [""]/flow_d4.gif, [""]/flow_d5.gif)

- - Thoughts on the page and illustrations:

- - - I like the use of color-coding to emphasize which variables provide the (direct) input values for the calculation of which other variables or, to phrase it the opposite way, which variables derive their values from which other variables. The use of different colors also provides a nice solution to the problem of how to address line crossings; if one wanted to be *really* rigorous, I suppose that one could note the crossing of two colored lines of nonzero thickness by giving their area of intersection the color that is intermediate between theirs.

- - - Subject to space limitations, it might be nice to a) label the colored lines with the mathematical relationships between the variables whose values are known and the variable whose value is either unknown or known only through other means and b) add a directionality element by converting the lines into arrows pointing away from the variables used in the calculation and toward the variable whose value is being calculated. These additions would help emphasize the data-flow aspect of the diagram and would give specificity to the relationships whose existence the diagram currently emphasizes.

- - - - For full detail and to emphasize the simultaneity of these relationships (i.e., the fact that they happen instantaneously rather than evolve over time), each relationship could then be labeled with two complementary arrows / arrow sets: a) one featuring multiple tails converging to a single shaft and head, pointing in the ""composition"" direction, and labeled with the equation for calculating the ""target"" variable's value [i.e., the arrow described above] and b) one featuring a single tail that diverges into multiple heads, each linking to a given known-value variable and labeled with the equation's rearranged version in which the known-value variable is being solved for. Although the diverging arrow in b) wouldn't itself ""carry"" the ""data flow"" of the other initially value-known variables needed to solve for the variable being pointed to by a given ""branch"" of the diverging arrow, conceptually speaking, one could account for the other variables by starting from each of them, following the above arrow to its point of convergence, and then turning around and following the diverging-arrow ""branch"" that leads to the variable being solved for in the rearranged equation.)

- - - - Such a diagram (especially one with ""two-way"" labeling) would be a good test-/exam-review material for students having difficulty with these basic concepts. It might be good to make explicit that constructing and labeling such a diagram would likewise be a good test-/exam-review exercise, one even better than studying a pre-existing diagram: You of course know this, at least implicitly -- after all, that's probably at least part of why you've asked this Question in the first place -- but it might be good to make sure that they know as well.

confidence rating #$&*: OK re: substance; between 1.5 and 2 re: which equation of motion gets the ""third"" label

@&

The order I use:

`ds = (vf + v0) / 2 * `dt, which is equivalent to the definition of average velocity

vf = v0 + a `dt, which is equivalent to the definition of average acceleration

(these first two are regarded as the most fundamental in the sense that they are bascially restatements of the definitions)

`ds = v0 `dt + 1/2 a `dt^2, which results from eliminating vf from the first two equations

vf^2 = v0^2 + 2 a `ds, which results from eliminating `dt from the first two.

These equations are understood to apply to some interval of uniform acceleration.

However if you approach this from the point of view of calculus, the most fundamental equations would follow from

v ' = a

and

x ' = v.

Integrating v ' = a we get

v = a t + v_0

and integrating s ' = v we get

x = 1/2 a t^2 + v_0 t + x_0,

where x_0 and v_0 are position and velocity at t = 0.

These equations reconcile with #'s 2 and 3 of the preceding list, for the special case where v stands for v_f and x - x_0 for `ds.

These equations are regarded as defining v and x as functions of t, so that we could write explicitly

v(t) = a t + v_0

x(t) = 1/2 a t^2 + v_0 t + x_0.

*@