Graph of approximation to velocity y - Uapprox (1) Using this graph, you can estimate the displacement of the object after x seconds have elapsed by the value of the function - J. U approx (t) dt. (A) Using the function s(x), answer the following questions about how far the object traveled. Your answers must include the correct units. Displacement after 6 seconds = Total displacement = Total distance traveled = (B) From the graph above, indicate the time interval or union of time intervals where the object is moving forward, backward, and is stationary. Enter your answer using interval notation. Forward: Backward: Stationary:(1 point) The velocity of a particle moving along a line is given by v(t) = t' - 2t- meters per second. Find the displacement of the particle during the time interval between -2 and 3 seconds. Displacement = (Include the correct units.) To find the total distance traveled by the particle during the time interval from -2 to 3 seconds, we must split the integral of the absolute value of velocity into a sum of two integrals 3 k otal distance traveled - / / 18 - 217\\at Cat - |2(t di where u1 (t) and U2(t) are functions and k is a number such that U1 (t) = (Absolute values are not allowed.) U2 (t ) = (Absolute values are not allowed.) k = Total distance traveled = (Include the correct units.)(1 point) The velocity of an object was measured using a laser radar gun. The following data were collected. time (sec) 0 1 2 3 4 5 6 7 8 velocity (feet/sec) -4 -1 - 1 -3 -3 - 1 0 0 1 You decide to plot these velocity data and connect successive data points with lines, as in the following graph. This graph determines a function U approx(t) that approximates the actual velocity function U actual (t), which is unknown. By connecting data points with lines in the graph you are assuming that velocity is changing at a constant rate over one-second time intervals (or, equivalently, that acceleration is constant over one-second time intervals). This assumption may be incorrect because the actual rate of change of velocity may not be constant over one-second time intervals. However, you decide to use this graph anyway since it seems like a reasonable approximation to the actual velocity. -1