Chapter 6, Problem 11RE

(a)

To determine

The body travel during those 10 seconds.

Answer to Problem 11RE

The value is ${\displaystyle \underset{0}{\overset{10}{\int }}f\left(x\right)}dx=26.5\text{meter}$

Explanation of Solution

Given information:

The accompanying graph shows the velocity (m/sec) of a body moving along the s-axis during the time interval from t= 0 to t=10 sec.

  

Formula used:

  $h=\frac{b-a}{n}$

Calculation:

Apply Simpson's rule, to approximate ${\displaystyle \underset{a}{\overset{b}{\int }}f\left(x\right)}dx$ , use

  $S=\frac{h}{3}\left(y_0+4y_1+2y_2+4y_3+\mathrm{.....}+2y_{n-2}+4y_{n-1}+y_n\right)$

Where [a, b] is partitioned into an even number n of subintervals of equal length $h=\frac{b-a}{n}$

Now,

Apply the Simpson’s rule with

  $\begin{array}{l}n=10\\ \left[a,b\right]=\left[0,10\right]\end{array}$

So,

  $\begin{array}{l}h=\frac{b-a}{n}\\ =\frac{10-0}{10}\\ h=1\end{array}$

The table shows

  

Now, substitute the values from given table in this equation

  $\begin{array}{l}{\displaystyle \underset{0}{\overset{10}{\int }}f\left(x\right)}dx=\text{total distance traveled}\\ \text{=}\frac{h}{3}\left(\begin{array}{l}{y}_0+4y_1+2y_2+4y_3+2y_4+4y_5\\ +2y_6+4y_7+2y_8+4y_9+y_{10}\end{array}\right)\\ =\frac{1}{3}\left(\begin{array}{l}0+4\left(0.5\right)+2\left(1\right)+4\left(2\right)+2\left(3.5\right)\\ +4\left(4.5\right)+2\left(4.75\right)+2\left(3.5\right)+4\left(2\right)+0\end{array}\right)\\ {\displaystyle \underset{0}{\overset{10}{\int }}f\left(x\right)}dx=26.5\text{meter}\end{array}$

Conclusion:

The value is ${\displaystyle \underset{0}{\overset{10}{\int }}f\left(x\right)}dx=26.5\text{meter}$

(b)

To determine

The graph of the position as the function of time t.

Answer to Problem 11RE

The graph gets increases continuously from the origin.

Explanation of Solution

Given information:

The accompanying graph shows the velocity (m/sec) of a body moving along the s-axis during the time interval from t= 0 to t=10 sec.

  

Formula used:

The x axis represents the horizontal axis and the y axis represents the vertical axis.

Calculation:

The required graph of the position as a function of time is:

  

Conclusion:

The graph gets increases continuously from the origin.