Chapter 1.1, Problem 44E

(a)

To determine

To write: The expression $d\left(t\right)$ for the distance of the car travel from $P$ .

Answer to Problem 44E

The expression $d\left(t\right)$ for the distance of the car travel from $P$ is $d\left(t\right)=45t$ .

Explanation of Solution

Given information: It is given that the car starts from point $P$ at time $t=0$ , and travels at $45\text{mph}$ .

Calculation:

It is known that if an object is travelling with constant speed $v$ , then the distance travel by that object in time $t$ is given by $d\left(t\right)=v\times t$ .

Substitute 4 for $t$ in the above formula for the distance of the car travel from $P$ .

  $d\left(t\right)=45t$

Therefore, the expression $d\left(t\right)$ for the distance of the car travel from $P$ is $d\left(t\right)=45t$ .

(b)

To determine

To plot: The graph of the equation $d\left(t\right)=45t$ .

Explanation of Solution

Given information: Consider the equation.

  $d\left(t\right)=45t$

Calculation:

Take the variable $t$ as $x$ . Use the following step to graph the parametric equations by graphing calculator.

Step 1: First press the “ON” button on graphical calculator.

Step 2: Press $\boxed{\text{Y=}}$ and set the equation $y=45t$ by pressing the keystrokes $\boxed{4}\boxed{5}\boxed{\text{X}}$ .

Step 3: Press $\boxed{\text{GRAPH}}$ to obtain the graph of the equations and the window can be set to $\left[0,6\right]$ by $\left[-50,300\right]$ as shown below.

  

Figure (1)

Interpretation: From the graph of the function $y=45t$ it can be observed that the function passes through the origin.

(c)

To determine

To find: The slope of the graph, and effect of slope on the car.

Answer to Problem 44E

The slope is $45$ , and it is the speed of the car in miles per hour.

Explanation of Solution

Given information: Consider the equation.

  $d\left(t\right)=45t$

Calculation:

Compare the equation $d\left(t\right)=45t$ with $y=mx+b$ .

  $m=45$

It is the speed of the car in miles per hour.

Therefore, the slope is $45$ , and it is the speed of the car in miles per hour.

(d)

To determine

To create: The scenario in which $t$ could have negative values.

Answer to Problem 44E

The scenario in which $t$ could have negative values is when the car passes $P$ , and the car started the trip.

Explanation of Solution

Given information: It is given that the car starts from point $P$ at time $t=0$ , and travels at $45\text{mph}$ .

Assume the car starts travelling from some other point towards point $P$ and takes $5$ hours to get there.

Let $t=0$ hour represent the time when the car passes $P$ . Then the car started the trip at $t=-5\text{hr}$ and all negative values. So, $-5<t<0$ represent the trip from the beginning point to $P$ .

Therefore, the scenario in which $t$ could have negative values is when the car passes $P$ , and the car started the trip.

(e)

To determine

To create: The scenario in which $y$ -intercept of $y=d\left(t\right)$ could be $30$ .

Answer to Problem 44E

The scenario in which $y$ -intercept of $y=d\left(t\right)$ could be $30$ is when the car starts at time $t=0$ at a point $30$ miles past $P$ .

Explanation of Solution

Given information: It is given that the car starts from point $P$ at time $t=0$ , and travels at $45\text{mph}$ .

The $y$ -intercept of the function means the distance between the car, and point $P$ , at $t=0$ .

In order to have the $y$ -intercept be $30$ , the car must starts at time $t=0$ at a point $30$ miles past $P$ .

Therefore, the scenario in which $y$ -intercept of $y=d\left(t\right)$ could be $30$ is when the car starts at time $t=0$ at a point $30$ miles past $P$ .