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[1 point} The motion of a spring that is subject to a frictional force or a damping force {such as a shock absorber on a car} is often modeled by the product of an exponential tunction and a sine or cosine function. Suppose the equation of motion of a point on such a spring is 5\"} = 221 3' sin[211') where s is measured in centimeters and t is measured in seconds. Find the velocity of the point after 2 seconds. vii-t} = Graph both thepos'rtion and the velocitytunctiontot 5 r5 2 andputa'rintheboitwhenycuaredone [1 point] A Cepheid variable star is a star whose brightness alternately increases and decreases. Suppose that Cephei Joe is a star for which the interval between times of maximum brightness is 5.? days. Its average brightness is 2.? and the brightness changes by +HCI.45. Using this data. we can construct a mathematical model for the brightness of Cephei Joe at time t. where t is measured in days: err} = 2.? + 0.45 sin(2xrt.?} {a} Find the rate of change of the brightness after I days. Rate of change = {b} Find the rate at increase after one day. Rate of increase = {1 point] At a time t seconds after it is thrown up in the air. a tomato is at a height [In meters} of ft!) = -4.9:2 + 40! + 4 m. A. What is the average velocity at the tomato during the first 3 seconds? {Include unite.) E. Find (exactly) the instantaneous velocity of the tomato at .t = 3. {Include units} C. What is the acceleration at r = 3? [Include mite.) D. How high does the tomato go? {Include units.) E. How long is the tomato In the air? (Include units}