Question

finding the total displacement and Total distance traveled

Your task is to estimate how far an object traveled during the time interval U X t X 8, but you only have the following data about the velocity of the object. time (sec) 012345 6 7 8 velocity (feet/sec) 1 2414-2-1-2-3 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. 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

Answer 1