A radar gun was used to record the speed of a runner during the first 5 seconds

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)
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]

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.