A race car moves such that its position fits the relationship x = (5 m/s)t + (0.
ID: 2164465 • Letter: A
Question
A race car moves such that its position fits the relationshipx = (5 m/s)t + (0.8 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 = 4.7 s, by computing the average velocity using a time interval of 0.40 s (i.e, in this case, the average velocity from 4.5 s to 4.9 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
?t = 0.20 s
?t = 0.10 s
(c) Compare the average velocity during the first 4.7 s with the results of (b).
The average velocity of m/s is the instantaneous velocity.
I don't even know where to start
Explanation / Answer
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