For all you professors out there

By Guillaume Pelletier on February 10, 2009

I guess there is a point in life when you get into more advanced courses and rudimentary definitions become trivial to the solution of equally more complex problems. However, I as a student think it is important to respect scientific rigor when solving a physics or mathematics problem. Here is a small reminder to all physics teachers of what they used to teach us back in highschool:

Obviously the distance is not always the same as the displacement vector...

Now of course there is an important difference between the length of a path and the displacement vector of the corresponding path. Thus there is also an equally important semantic difference to be made between the two concepts.

Let us define for a parametric function f such that f \left( t \right) ={x \left( t \right) ,y \left( t \right) } describes the motion of an object, as was traditionally done countless years back, the distance s in time t as:

s=\int_0^t \! \sqrt {{ \left ( {\frac {{\it dx}}{{\it dt}}} \right ) }^{2}+{ \left ( {\frac {{\it dy}}{{\it dt}}} \right ) }^{2}} \, dt

For the same function f we have the displacement vector \vec{d} defined as:

\vec{d}=\int_0^t \! 1 \, dt

Please, please, science is not like litterature; if you want us to calculate the displacement vector, tell us to calculate the “displacement vector”; if you want us to calculate the distance along a path, then you can use the word “distance”. For the sake of scientific rigor, respect the conventions and don’t try to make fancy ambiguous sentences.

Seriously, it’s not like it would kill you. As of me, on the other hand, we never know! I might end up having lost a crucial 6% in an examination paper, and because of such ambiguity, I might not end up going to McGill two years from now, at which point I might or might not be part of a car accident in Moncton. Now I understand the probability of that happening is rather scarce, but let’s just play it on the safe side, shall we?

Posted in University