A radar gun was used to record the speed of a runner during the first 5 seconds
ID: 2845958 • Letter: A
Question
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
answer in meters
Given.
t (s) v (m/s) 0 0
3.0 10.59 0.5 4.67
3.5 10.69 1.0 7.38
4.0 10.78 1.5 8.86
4.5 10.81 2.0 9.73
5.0 10.81 2.5 10.24
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 How large do we have to choose n so that the approximations Tn and Mn to the integral are accurate to within 0.0001? (Use the fact that the range of the sine and cosine functions is bounded by plusminus 1 to estimate the maximum error.)
Explanation / Answer
To get the distance covered, integrate the velocity function :
x = int[v(t)] dt
We can use Simpson's Rule to approximate this integral for the given data points.
x = (?t/3)[v0 + 4v1 + 2v2 + 4v3 + 2v4 + 4v5 + 2v6 + 4v7 + 2v8 + 4v9 + v10]