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(1 pt) Your task is to estimate how far an object traveled during the time interval 0 S158, but you only have the following data about the velocity of the object.
time (sec) 0 1 2 3 4 5 6 7 8
velocity (feet/sec)-4-21243421
To get an idea of what the velocity function might look like, you pick up a black pen, plot the data points, and connect them by curves. Your sketch looks something like the black curve
in the graph below.
110
Left endpoint approximation
You decide to use a left endpoint Riemann sum to estimate the total displacement. So, you pick up a blue pen and draw rectangles whose height is determined by the velocity
measurement at the left endpoint of each one second interval. By using the left endpoint Riemann sum as an approximation, you are assuming that the actual velocity is approximately
constant on each one second interval (or equivalently, that the actual acceleration is approximately zero on each one-second interval), and that the velocity and acceleration have
discontinuous jumps every second. This assumption is probably incorrect because it is likely that the velocity and acceleration change continuously over time. However, you decide to
use this approximation anyway since it seems like a reasonable approximation to the actual velocity given the limited amount of data.
(A) Using the left endpoint Riemann sum, find approximately how far the object traveled. Your answers must include the correct units.
Total displacement =
Total distance traveled =
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