- Imagine a road on which the speed limit is specified at
every single point. In other words, there is a certain function $L$
such that the speed limit $x$ miles from the beginning of the road is
$L(x)$. Two cars A and B, are driving along this road; car A's
position at time $t$ is $a(t)$, and car B's is $b(t)$.
- What equation expresses the fact that the car A always
travels at the speed limit?
(Hint: the answer is {not} $a'(t)=L(t)$.)
- Suppose that A always goes at the speed limit, and that
B's position at time $t$ is A's position at time $t-1$. Show that B
is also going at the speed limit at all times.
- Suppose B always stays at a constant distance behind A.
Under what circumstances will B still always travel at the speed limit?
Tags: t1,c2,A,word-problem,composite-function,derivative,chain-rule,forming-a-strategy,multistep-problem, utf07-004
This is an interesting extension of
utf07-004. –
Eric Hsu 2008-07-12 21:03