Time (seconds) | 0 | 1 | 2 | 3 | 4 | 5 | 6 |

Speed (mph) | 0 | 5 | 15 | 25 | 40 | 50 | 60 |

distance rate time

We overestimate by assuming the velocity is a constant
equal to the max on each interval:
estimate miles

(Note: there are seconds in an hour.)
But
, so the article is inconsistent. (Doesn't
this sort of thing just bug you? By learning calculus you'll
be able to double-check things like this much more easily.)
**Insight!** *The formula for the estimate of distance traveled
above looks exactly like an approximation for the area under
the graph of the speed of the car!* In fact, if an object
has velocity at time , then the net change in position
from time to is

We'll come back to this observation frequently.

William Stein 2006-03-15