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

Question

A blue car is moving forward along a straight line. The distance the blue car travels (in meters) from its starting position \(t\) seconds after it started moving is given by \(s(t) = 5t^2\). Suppose the red car travels at a constant speed and travels a distance of \(1375\) meters on the interval \([7,18]\).

Select each of the true statements from the following:

Answerlist

  • The constant rate of the red car is \(125\)

  • The average speed of the blue car on this interval is the same as the constant speed of the red car.

  • The average speed of the blue car on the interval \([7,18]\) is greater than \(s(7)\).

Solution

Answerlist

  • True. The constant rate of the red car is the distance it traveled over the interval \(t=7\) to \(t=18\) divided by the length of this interval which is \(\frac{1375}{11} = 125\)

  • True. The blue car also travels a distance of \(1375\) meters over the interval \([7,18]\). Therefore, the average speed of the blue car on this interval is the same as the constant speed of the red car.

  • False. The average speed of the blue car on the interval \([7,18]\) is \[ \frac{s(18)-s(7)}{18-7} = \frac{1620 - 245}{11}= 125 \] which is less than \(s(7)=\) 245

Meta-information

extype: mchoice exsolution: 110 exname: AverageRateOfChange