91Ó°ÊÓ

The given table is,

As we know that the acceleration of any body is the ratio of change of velocity and the time.

The velocity of parachutist at $t=1$is 9 meters per second.

Calculate the acceleration using the above data.

$$\begin{gathered} a\left(t\right)=\frac{9}{1} \\ =9 \end{gathered}$$

The velocity of parachutist at $t=2$is 17 meters per second.

Calculate the acceleration using the above data.

$$\begin{gathered} a\left(t\right)=\frac{17}{2} \\ =8.5 \end{gathered}$$

The velocity of parachutist at $t=3$is 23 meters per second.

Calculate the acceleration using the above data.

$$\begin{gathered} a\left(t\right)=\frac{23}{3} \\ =7.66 \end{gathered}$$

The velocity of parachutist at $t=4$is 28 meters per second.

Calculate the acceleration using the above data.

$$\begin{gathered} a\left(t\right)=\frac{28}{4} \\ =7 \end{gathered}$$

The acceleration of the parachutist decreases as the value of time increases. It implies that the change in velocity is low. Thus, velocity increases slowly.

It is given that the curve of velocity function is in the shape of the concave down.

The trapezoid and midpoint sums of the function related as $TRAP\left(n\right)≤{∫}_a^{b}f\left(x\right)dx≤MID\left(n\right)$

Write an inequality on the given situation that is $TRAP\left(n\right)≤{∫}_0^{4}v\left(t\right)dt≤MID\left(n\right)$

The velocity of parachutist is 0 for $t=0$

Use the formula for Trapezoid and midpoint sum to calculate the value,

$$\begin{gathered} TRAP\left(n\right)=\frac{1}{2}\left(f\left(0\right)+f\left(1\right)+f\left(2\right)+f\left(3\right)+f\left(4\right)\right) \\ =\frac{1}{2}\left(0+2\left(9\right)+2\left(17\right)+2\left(23\right)+28\right) \\ =\frac{126}{2} \\ =63 \\ And \\ MID\left(n\right)=1\left(f\left(\frac{0+1}{2}\right)+f\left(\frac{1+2}{2}\right)+f\left(\frac{2+3}{2}\right)+f\left(\frac{3+4}{2}\right)\right) \\ =f\left(\frac{1}{2}\right)+f\left(\frac{3}{2}\right)+f\left(\frac{5}{2}\right)+f\left(\frac{7}{2}\right) \\ =4.5+13+20++25.5 \\ =63 \end{gathered}$$

Thus, the possible lower and upper bound is equal to 63.