A radio controlled experimental vehicle is tested on a straight track. It starts from rest, and its velocity v (meters per second)is recorded in the table every 10 seconds for a minute.

t: 0 10 20 30 40 50 60
v: 0 5 21 40 62 78 83
(^ thats supposed to be a table)

a. Use a graphing utility to find the model of the form v=at^3+bt^2+ct+d for the data.

b. Use a graphing utility to plot the data and graph the model.

c. Use the fundamental theorem of calculus to approximate the distanced traveled by the vehicle during the test.

Question

A radio controlled experimental vehicle is tested on a straight track. It starts from rest, and its velocity v (meters per second)is recorded in the table every 10 seconds for a minute.

t: 0 10 20 30 40 50 60 
v: 0 5 21 40 62 78 83
(^ thats supposed to be a table)

a. Use a graphing utility to find the model of the form v=at^3+bt^2+ct+d for the data.

b. Use a graphing utility to plot the data and graph the model.

c. Use the fundamental theorem of calculus to approximate the distanced traveled by the vehicle during the test.

anonymous · Answer

fundamental theorem of calc is hinting that you use an integral. The chart above suggests a discrete sum of certain strings of data, the integral is a sum as well, but over a continuous spectrum of values. An integral from say, 1 to 10, can be used as an approximation of 1+2+3+...10. The statistical part simply means you should use a regression line utility to generate a least squared means line fit, but in this case it isn't a line, it is of that weird cubic form above, just use mathematica or a program's regression analysis best fit least regression app and ask it for a fit of the above form.