The velocity of a cheetah over one minute, measured every 10 seconds, is given in the table below.
Estimate the distance the cheetah travels during this minute.
Since the problem doesn't specify what type of sum to use, we'll use a trapezoid sum.
When we're trying to figure out how far a cheetah runs in one minute, our estimates get more accurate as we measure the velocity more frequently. If all we know is that the cheetah was going 0 feet per second at the beginning of the minute and 50 feet per second at the end of the minute, our best guess is that the cheetah went about 25 feet per second for the whole minute, for a total of
25(60) = 1500 feet.
If we measure the velocity every ten seconds, then we get a better idea of what the cheetah's velocity is doing:
Measuring the velocity every 10 seconds lets us see that the velocity goes above 50 feet per second.
If we measure the velocity every 5 seconds, we get an even better idea of what's going on: