units on t

[Alex Jordan]

In section 5.4, there are some exercises that give a velocity formula like:
v(t) = -32t + 20 ft/s
and ask to find the net displacement over an interval like [0,5].

It is implied from this that t is measured in seconds, and the
interval [0,5] covers quantities in seconds. But it's not explicit.
Certainly there would be applications where something like [0,2] could
be in days, but the formula is in miles/hour or something like that,
where the units don't directly match.

Should these stay as they are? Is inferring the unit on "t" part of
the exercise? Or would explicitly stating the unit on t be an
improvement?

[Sean Fitzpatrick]

I think it wouldn't hurt to mention the unit, but I suppose this one is up to Greg.

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[gregory...@gmail.com]

We should specify the units as it reinforces the idea that units matter and one should always check. 

The problem "v(t) = -32t+20ft/s on [0,5]" could be rewritten as 

"v(t) = -32t + 20ft/s, where t is measured in seconds on [0,5]." I think that establishes both 1) what t represents, and 2) that [0,5] is also an interval representing seconds.

Related: in that exercise set, all velocities are ft/s save one, which is mph. I think one more exercise (likely #43, which is "v(t) = 10ft/s on [0,3]") should have its units change to mph.