1.
Distance Traveled Problem
(SO)
Suppose a car is moving with non-decreasing speed according to the table below.
Time (sec.)
0 2 4 6 8 10
Speed (ft. / sec.) 30 36 40 48 54 60
(a)
What is an upper estimate for the distance traveled in the first 2 seconds?
(b)
Determine upper and lower estimates for the change in position for the first 10 seconds.
(c)
If you choose your lower estimate as your guess for the change in position, what is the
maximum possible error?
(d)
How could we use a lower estimate and be sure our maximum possible error is less?
(e)
Makeup speeds to correspond with t 1, 3, 5, 7, 9 . Keep the non-decreasing nature of the
speeds and do not use the average of pairs of speeds from the existing table. Recalculate the
upper and lower estimates.
(f)
What happened to the maximum error in using the lower estimate as your guess for the
change in position?
(g)
How often would you need to measure the speed in order for the lower estimate for the
change in position to be off by less than one foot?