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) v (m/s)|t (s) v (m/s) 3.0 10.54 0.5 4.68 3.5 10.68 1.0 7.37 4.0 10.77 1.5 8.87 4.5 10.82 2.0 9.74 5.0 10.82 2.5 10.25 Step 1 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 =s andn = 10 v 10 subintervals. Step 2 Simpson's Rule says that f(x) dx * Snr S, = AX [f(xo) + 4f(x1) + 2f(x2) +. + 2f(xn - 2) + 4f(xXp - 1) + f(xn)]. We will use the table to find values for v(t). For example, when t = 1.5, we have v(1.5) = 8.87 8.87 m/s. Step 3 Therefore, distance= v(t) dt 1 [0 + 4(4.68) + 2(7.37) + 4(8.87) + ... + 10.82] 6 m (rounded to three decimal places). Submit Skip (you cannot come back)
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) v (m/s)|t (s) v (m/s) 3.0 10.54 0.5 4.68 3.5 10.68 1.0 7.37 4.0 10.77 1.5 8.87 4.5 10.82 2.0 9.74 5.0 10.82 2.5 10.25 Step 1 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 =s andn = 10 v 10 subintervals. Step 2 Simpson's Rule says that f(x) dx * Snr S, = AX [f(xo) + 4f(x1) + 2f(x2) +. + 2f(xn - 2) + 4f(xXp - 1) + f(xn)]. We will use the table to find values for v(t). For example, when t = 1.5, we have v(1.5) = 8.87 8.87 m/s. Step 3 Therefore, distance= v(t) dt 1 [0 + 4(4.68) + 2(7.37) + 4(8.87) + ... + 10.82] 6 m (rounded to three decimal places). Submit Skip (you cannot come back)
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter3: The Derivative
Section3.4: Definition Of The Derivative
Problem 50E
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![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) v (m/s)|
t (s) v (m/s)
3.0
10.54
0.5
4.68
3.5
10.68
1.0 7.37
4.0
10.77
1.5 8.87
4.5
10.82
2.0
9.74
5.0
10.82
2.5
10.25
Step 1
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 =
s and n = 10
10 subintervals.
Step 2
Simpson's Rule says that
f(x) dx Sn,
S, = AX [f(xo) + 4f(x1) + 2f(x2) + ... + 2f(x, – 2) + 4f(xXn – 1) + f(xn)].
We will use the table to find values for v(t). For example, when t = 1.5, we have
v(1.5) = 8.87
8.87 m/s.
Step 3
Therefore,
distance =
v(t) dt
1
[0 + 4(4.68) + 2(7.37) + 4(8.87) + ... + 10.82]
6
m (rounded to three decimal places).
Submit
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Transcribed Image Text: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) v (m/s)|
t (s) v (m/s)
3.0
10.54
0.5
4.68
3.5
10.68
1.0 7.37
4.0
10.77
1.5 8.87
4.5
10.82
2.0
9.74
5.0
10.82
2.5
10.25
Step 1
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 =
s and n = 10
10 subintervals.
Step 2
Simpson's Rule says that
f(x) dx Sn,
S, = AX [f(xo) + 4f(x1) + 2f(x2) + ... + 2f(x, – 2) + 4f(xXn – 1) + f(xn)].
We will use the table to find values for v(t). For example, when t = 1.5, we have
v(1.5) = 8.87
8.87 m/s.
Step 3
Therefore,
distance =
v(t) dt
1
[0 + 4(4.68) + 2(7.37) + 4(8.87) + ... + 10.82]
6
m (rounded to three decimal places).
Submit
Skip (you cannot come back)
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