#output:
## html_document: default
# pdf_document: default
## put rmarkdown::render(“this_file.Rmd”) at the R command line to compile

Question

An object is moving forward along a straight line. The distance the object has traveled (in meters) from its starting position \(t\) seconds after it started moving is given by \(s(t) = 2\sqrt{t}\). What is the average velocity of the object over the interval from \(t = 7\) to \(t = 17\)

Select each of the true statements from the following:

Answerlist

  • \(s(7)=8.24621125123532\)

  • \(s(17)-s(7) = 2.95470862910614\)

  • \(s(7)=5.29150262212918\)

  • The average velocity of the object over the interval \([7,17]\) is \(2.95470862910614\)

  • The average velocity of the object over the interval \([7,17]\) is \[ \frac{s(17) - s(7)}{17-7} \].

Solution

Answerlist

  • False. \(s(7) = 2\sqrt{7} = 5.29150262212918\)
  • True. \(s(17)-s(7) = 5.29150262212918 - 8.24621125123532 = 2.95470862910614\)
  • False. \(s(17) = 2\sqrt{17} = 8.24621125123532\)
  • False. The average velocity of the object over \([a,b]\) is \[ \frac{s(b)-s(a)}{b-a} \] Set \(a=7\) and \(b=17\) then the average velocity of the object over the interval \([a,b] = [7,17]\) is \[ \frac{s(b)-s(a)}{b-a} = \frac{s(17) - s(7)}{17-7} =\frac{8.24621125123532 - 5.29150262212918}{10} = 0.295470862910614 \].
  • True. The average velocity of the object over \([a,b]\) is \[ \frac{s(b)-s(a)}{b-a} \] Set \(a=7\) and \(b=17\) then the average velocity of the object over the interval \([a,b] = [7,17]\) is \[ \frac{s(b)-s(a)}{b-a} = \frac{s(17) - s(7)}{17-7} \].

Meta-information

extype: mchoice exsolution: 01001 exname: Average Velocity