A race car moves such that its position fits the relationship x = (5 m/s)t + (0.

Question

A race car moves such that its position fits the relationship x = (5 m/s)t + (0.7 m/s3)t3 where x is measured in meters and t in seconds. (a) Plot a graph of the car's position versus time. (Do this on paper. Your instructor may ask you to turn in this work.) (b) Determine the instantaneous velocity of the car at t = 4.8 s, by computing the average velocity using a time interval of 0.40 s (i.e, in this case, the average velocity from 4.6 s to 5 s. Repeat for time intervals of .20 s, and .10 s. In order to better see the limiting process keep exactly five significant figures in your answer). ?t = 0.40 s _______m/s ?t = 0.20 s _______ m/s ?t = 0.10 s _______m/s (c) Compare the average velocity during the first 4.8 s with the results of (b). The average velocity is ______m/s

Explanation / Answer

Please change the values What you are doing is finding ?x/?t as ?t approaches 0 We have x(3.1) = 38.507 Now find x(3.5) = 52.439 so ?x/?t = (52.439 - 38.507)/0.4 = 34.8 now find x(2.7) = 27.463 so ?x/?t = (38.507-27.463)/0.4 = 27.6 So (34.8 + 27.6)/2 = 31.2m/s

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