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Question

# A car is traveling at 80 feet per second (approximately 55 miles per hour) and slows down as it passes through a busy inter section. The car's velocity is shown in the following table.$\begin{array}{c|c|c|c|c|c|} \hline \text { Time since brakes applied (seconds) } & {0} & {3} & {6} & {9} & {12} \\ \hline \text { velocity (ft/sec) } & {80} & {62} & {47} & {32} & {22} \\ \hline \end{array}$Use a left sum to approximate the total distance the car has traveled over the 12 second interval.

Solution

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For constant velocity the distance is given by

$\text{Distance}=\text{Velocity}\times \text{Travel Duration}$

this means we can approximate the total distance travelled with a left sum as such

\begin{align*} \text{Left estimate} &= \sum \text{Left value velocity} \cdot \Delta t \\ &= 80(3-0) + 62(6-3) + 47(9-6) + 32(12-9) \\ &= 663 \; \text{ft} \end{align*}

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