121616949-math.40 - 26 Chapter 2 Instantaneous Rate Of...

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26 Chapter 2 Instantaneous Rate Of Change: The Derivative Exercises 1. An object is traveling in a straight line so that its position (that is, distance from some fixed point) is given by this table: time (seconds) 0 1 2 3 distance (meters) 0 10 25 60 Find the average speed of the object during the following time intervals: [0 , 1], [0 , 2], [0 , 3], [1 , 2], [1 , 3], [2 , 3]. If you had to guess the speed at t = 2 just on the basis of these, what would you guess? 2. Let y = f ( t ) = t 2 , where t is the time in seconds and y is the distance in meters that an object falls on a certain airless planet. Draw a graph of this function between t = 0 and t = 3. Make a table of the average speed of the falling object between (a) 2 sec and 3 sec, (b) 2 sec and 2.1 sec, (c) 2 sec and 2.01 sec, (d) 2 sec and 2.001 sec. Then use algebra to find a simple formula for the average speed between time 2 and time 2 + Δ t . (If you substitute Δ t = 1 , 0 . 1 , 0 . 01 , 0 . 001 in this formula you should again get the answers to parts (a)–(d).)
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