CPM Homework Help : APCALC Problem 3-121

While testing the brakes of a new car, Badru recorded the following speeds traveled (in miles per hour) over time (in seconds). Approximately how far did Badru’s car travel before stopping?

$\boldsymbol t$ (seconds)	$0$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$\boldsymbol {v(t)}$ (mph)	$50$	$48$	$46$	$43$	$40$	$37$	$34$	$29$	$23$	$14$	$0$

Hint:

Notice the units. Time is given in seconds, but velocity is given in miles per hour.

Hint:

Distance traveled can be found by calculating area under a velocity graph. Since we cannot see the graph and do not know the function, we must approximate the area given the select values in the table.

Hint:

Which do you think will give the most accurate approximation: rectangles or trapezoids?

Hint:

The Trapezoid Rule

The Trapezoid Rule can be used to approximate the area under a curve if the widths, $\Delta x$ , of all trapezoids are of equal size:

$\left. \begin{array} { r } { A = \frac { \Delta x } { 2 } ( f ( a ) + 2 f ( a + \Delta x ) + 2 f ( a + 2 \Delta x ) + \ldots } \\ { + 2 f ( b - \Delta x ) + f ( b ) ) } \end{array} \right.$