A radar gun was used to record the speed of a runner during the first 5 seconds of a race (see the table). Use Simpson's Rule to estimate the distance the runner covered during those 5 seconds:
t (s)
(m/s) t (s)
(m/s) 10.54
3.0
0.5 4.68
3.5
10.68
1.0
7.31
4.0
10.71
1.5 8.83
4.5
10.88
2.0
9.78
5.0
10.88
2.5
10.23
The distance covered by the runner can be found by the integral of the velocity function evaluated over the time interval, distance v(t) dt.
Using the table provided, we will approximate this using Simpson's Rule with At = subintervals
s and
Step