ESSENTIAL CALCULUS(LL)-W/ACCESS>CUSTOM<
2nd Edition
ISBN: 9781337058742
Author: Stewart
Publisher: CENGAGE C
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Chapter 5, Problem 44RE
To determine
To calculate: The distance covered by the runner during 5 seconds with Midpoint rule.
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The speed of a runner increased steadily during the first three seconds of a race. Her speed at half-second intervals is given in the table. Find lower and upper estimates for the distance (in ft) that she traveled during these three seconds.
t (s)
0.5
1.0
1.5
2.0
2.5
3.0
v (ft/s)
5.7
11.2
15.5
18.8
19.4
20
lower
ft
upper
ft
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).
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Chapter 5 Solutions
ESSENTIAL CALCULUS(LL)-W/ACCESS>CUSTOM<
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