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. (Round your answer to three decimal places.)
t(s) v(m/s)
0 0
0.5 4.63
1.0 7.34
1.5 8.88
2.0 9.77
2.5 10.28
3.0 10.57
3.5 10.63
4.0 10.76
4.5 10.89
5.0 10.89

Answer 1

Answer:

44.835 meters

Step-by-step explanation:

From the table, we have that:

b = 5, a = 0, n = 10.

The Simpson's Rule is written in the equation below:

$estimated\ distance = (b -a) (f(0) + 4f(0.5) + 2f(1) + 4f(1.5) + 2f(2) + 4f(2.5) + 2f(3) + 4f(3.5) + 2f(4) + 4f(4.5) + f(5))/(3n)$

So substituting the values, we have that:

$estimated\ distance = (5-0)* (0 + 4*4.63 + 2*7.34 + 4*8.88 + 2*9.77 + 4*10.28 + 2*10.57 + 4*10.63 + 2*10.76 + 4*10.89 + 10.89)/(3*10)$

$estimated\ distance = 44.835\ meters$

So the estimated distance the runner covered during this 5 seconds is 44.835 meters

Answer 2

The required estimated distance the runner covered during this 5 seconds is 44.835 meters.

We have to determine, seconds of a race (see the table). Use Simpson's Rule to estimate the distance the runner covered during those 5 seconds.

According to the question,

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

t(s)         0   0.5     1.0    1.5    2.0    2.5     3.0      3.5     4.0      4.5      5.0

v(m/s)     0  4.63  7,34  8.88  9.77  10.28  10.57  10.63  10.76  10.89   10.89

Here,

n = 10

a = 0

b = 5

Then,

By using Simpson's Rule to estimate the distance the runner covered during those 5 seconds.

Estimated distance;

$=\frac{ (b-a) f(0)+ 4f (0.5) +2f(1) +4f(1.5) +2f(2)+ 4f(2.5) + 2f(3)+ 4f(3.5) + 2f(4) + 4f(4.5) + f(5)}{{3n}}$

Substitute the given values in the equation,

$=\frac{(5-4) \times ( 0+4 \times 4.63 + 2 \times 7.34 + 4 \times 8.88 +2 \times 9.77+ 4 \times 10.28 + 2 \times 10.57 + 4 \times 10.63 + 2 \times 10.76 + 4 \times 10.89 + 10.89)} {3 \times10}\\\\= 43.835 \ meter$

Hence , The required estimated distance the runner covered during this 5 seconds is 44.835 meters.

To know more about Simpson's rule click the link given below.

https://brainly.com/question/16871801