An object's distance vs. time function is given by 3 f(t) m 1 + t a) Using Desmos, plot the average velocity of the object over an interval of time of length h beginning at time t = : 2. b) Write down a limit that gives the instantaneous velocity of the object at t = 2. You do not need to simplify or compute this limit, but your answer should not contain an f. Without computing the limit, can you say whether it will be positive or negative? c) A portion of the graph of f (t) is shown below. Explain to another person in your tutorial section where and how each element of your answer to part (b) corresponds to a part of the graph. What happens as you take the limit? 2. Toy Car 2.5 2 1.5 1 0.5 0.5 0 0.5 1 1.5 2 2.5 3 3.5 4 A toy car is traveling at a constant speed of 5 ft/sec, travels 17 feet. a) The track is marked with intervals of length 1 ft. How many seconds does the car spend in each interval? b) The track is marked with intervals of length 1/500 ft. How many seconds does the car spend in each interval? c) The track is marked with intervals of length 1/2500 ft. How many seconds does the car spend in each interval? d) The track is marked with intervals of length Ax ft. How many seconds does the car spend in each interval? 3. Real Car The photo of the black car below was taken with the camera shutter open for 1/20 sec (that is, at 1/20th second exposure). The distance between white stripes is 3 m. The length of the blur is the distance the car traveled while the shutter was open.