Question

the table shows speedometer readings at 10 - second intervals during a 1 - minute period for a car racing at the daytona international speedway in florida. (a) estimate the distance the race car traveled during the 1 - minute period using the velocities at the end of the time intervals. hint: 1 mi/h=(5280/3600) ft/s. (round your answer to two decimal places.) mi illustrate your estimate by drawing a possible velocity curve and rectangles corresponding to your calculations.

Explanation:

Step1: Convert time - interval to hours

The time - interval $\Delta t$ between each measurement is $10$ seconds. Since $1$ hour = $3600$ seconds, then $\Delta t=\frac{10}{3600}=\frac{1}{360}$ hours.

Step2: Use the right - endpoint Riemann sum formula for distance

The formula for distance $d$ using a right - endpoint Riemann sum is $d=\sum_{i = 1}^{n}v(t_i)\Delta t$, where $v(t_i)$ is the velocity at the end of the $i$th time - interval and $\Delta t$ is the time - interval.
We have the following velocities: $v_1 = 182.9$ mph, $v_2=168.0$ mph, $v_3 = 106.6$ mph, $v_4=99.8$ mph, $v_5 = 124.5$ mph, $v_6=176.1$ mph, $v_7=175.6$ mph.

Step3: Calculate the sum

$d=\Delta t(v_1 + v_2+v_3+v_4+v_5+v_6+v_7)$
$d=\frac{1}{360}(182.9 + 168.0+106.6+99.8+124.5+176.1+175.6)$
$d=\frac{1}{360}(933.5)$
$d\approx2.59$ miles

Answer:

$2.59$ miles