Chapter 9.8, Problem 21PPS

(a)

To determine

To calculate: To graph the function on the coordinate plane.

Answer to Problem 21PPS

Graph is plotted

Explanation of Solution

Given information: Function $d=\frac{1}{2}a{t}^2$ represents the distance $d$ that a race car will travel over an amount of time $t$ given the rate of acceleration $a$

Calculation:

Function is given as

  $d=\frac{1}{2}a{t}^2$

Also, given that car is accelerating at a rate of $7$ feet per second

Substituting value of $a=7$ in above equation:

  $\begin{array}{l}d=\frac{1}{2}\left(7\right)t^2\\ d=\frac{7}{2}{t}^2\end{array}$

Now, in order to graph the equation, let’s find the points on the graph

When $t=0$

  $\begin{array}{l}d=\frac{7}{2}{\left(0\right)}^2\\ d=0\end{array}$

When $t=2$

  $\begin{array}{l}d=\frac{7}{2}{\left(2\right)}^2\\ d=7\times 2\\ d=14\end{array}$

When $t=4$

  $\begin{array}{l}d=\frac{7}{2}{\left(4\right)}^2\\ d=7\times 8\\ d=56\end{array}$

Function table is

x	Y
0	0
2	14
4	56

Plotting the points on graph:

  

Conclusion:

Hence, graph is plotted

(b)

To determine

To calculate: To find the time it would take the car to travel $125$ feet

Answer to Problem 21PPS

Thecar would take $5.97$ seconds to travel $125$ feet.

Explanation of Solution

Given information: Function $d=\frac{1}{2}a{t}^2$ represents the distance $d$ that a race car will travel over an amount of time $t$ given the rate of acceleration $a$

Calculation:

Function is given as

  $d=\frac{1}{2}a{t}^2$

Also, given that car is accelerating at a rate of $7$ feet per second

Substituting value of $a=7$ in above equation:

  $\begin{array}{l}d=\frac{1}{2}\left(7\right)t^2\\ d=\frac{7}{2}{t}^2\end{array}$

Graph of the equation is as follows:

  

From graph, car would take $5.97$ seconds to travel $125$ feet.

Conclusion:

Hence, car would take $5.97$ seconds to travel $125$ feet.