The graph of the velocity (in km/h) of a car that is accelerating is shown in the figure, where t is measured in seconds. (a) Use the midpoint rule with n = 3 to estimate the average velocity vave (in km/h) of the car during the first 12 seconds. vave = km/h (b) At what time t (in s) was the instantaneous velocity equal to the average velocity? (Round your answer to one decimal place.) t = s
![The displacement (in centimeters) of a particle s moving back and forth along a straight line is given by the equation s = 2 sin(πt) + 4 cos(πt), where t is measured in seconds. (Round your answers to two decimal places. ) (a) Find the average velocity during each time period. (i) [1, 2] cm/s (ii) [1, 1.1] cm/s (iii) [1, 1.01] cm/s (iv) [1, 1.001] cm/s (b) Estimate the instantaneous velocity of the particle when t = 1. cm/s](https://www.doubtrix.com/uploads/editor/9947714394TPgahcSJtp.png)
![A silver dollar is dropped from the top of a building that is 1393 feet tall. Use the position function below for free-falling objects. s(t) = −16t2 + v0t + s0 (a) Determine the position and velocity functions for the coin. s(t) = v(t) = (b) Determine the average velocity on the interval [2, 3]. ft/s (c) Find the instantaneous velocities when t = 2 seconds and t = 3 seconds. v(2) = ft/s v(3) = ft/s (d) Find the time required for the coin to reach the ground level. (Round your answer to three decimal places. ) t = s (e) Find the velocity of the coin at impact. (Round your answer to three decimal places.) ft/s](https://www.doubtrix.com/uploads/editor/1415542277QUpbdUsFqy.jpg)
