Consider the particle with position function s(t)= t3 t, where time, t, is measured in seconds...

 

 

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Consider the particle with position function s(t)= t3 t, where time, t, is measured in seconds and position at time t, s(t), is measured in feet.. (a) Find the average velocities of the particle on time intervals [0, 1] and [1,2]. Give an interpretation of these results using complete sentences and units from the given context. (b) Estimate the instantaneous velocity when t = 2 by filling in the following table of average velocities on the time intervals [1,1+h] and looking for a pattern as h approaches zero. 0.5 h Average Velocity on [2,2 + h] Give an interpretation of this result using a complete sentence and units from the given context. (c) Sketch the graph of s(t) along with a geometric interpretation of the result in part (a) and the instan- taneous velocity from part (b). Explain your solution carefully. 0.1 0.01 0.001 Consider the particle with position function s(t)= t3 t, where time, t, is measured in seconds and position at time t, s(t), is measured in feet.. (a) Find the average velocities of the particle on time intervals [0, 1] and [1,2]. Give an interpretation of these results using complete sentences and units from the given context. (b) Estimate the instantaneous velocity when t = 2 by filling in the following table of average velocities on the time intervals [1,1+h] and looking for a pattern as h approaches zero. 0.5 h Average Velocity on [2,2 + h] Give an interpretation of this result using a complete sentence and units from the given context. (c) Sketch the graph of s(t) along with a geometric interpretation of the result in part (a) and the instan- taneous velocity from part (b). Explain your solution carefully. 0.1 0.01 0.001