[Physltest] [Phys-L] Re: sign of velocity (was: California standards test in physics)

[John Denker <jsd@AV8N.COM>]

Rick Tarara wrote:
> I'm going to quibble here.  John is correct concerning the mathematics of
> vectors, but conceptually I think there is some wiggle room here.  Is the
> velocity at the end of the trip really less than the velocity at the start?
> (assuming up is taken as positive)  Again, mathematically yes, but
> conceptually I think we could look at it as the upwards velocity at the
> start is 'the same' as the downward velocity at the end.

OK, I'll take the quibble-bait.

1) It's comparing apples and oranges to compare the upward
component of velocity at the start to the downward component
of velocity at the end.  Unless you've got a good way of
making that systematic, it makes about as much sense as
comparing the upward comppnent at the start to the sideways
component at the end.

2) Ah, you might say, we are focussing here on the _forward_
component of velocity.  Well then I say, that has a perfectly
good name.  It's called the _speed_.  If you mean speed, say
speed.  Don't confuse speed with velocity.

> While we are
> talking about the speed here, the idea is that positive and negative are
> ARBITRARY labels to separate directions (after all we could have chosen down
> as positive) and being too pedantic about negative being less than positive
> can be confusing here.

The choice of whether upward or downward counts as positive
velocity (in one dimension) does not affect the analysis of
the question.  None of the answers make sense, no matter
which choice you make.

> How mathematical one needs to be here depends on the level of the course.  I
> would expect my Calculus level class to see the final velocity here as less
> than the initial velocity and might ask such a question.  With my Gen-Ed
> class, I would have no such expectation and therefore I don't ask the
> question.  I do ask about the speed at the start and end of this motion
> however.

Yes, that's the only sensible way out of the mess.  When you want
to talk about speed, call it speed.
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