Chapter 0.1, Problem 44E

(a)

To determine

To find: Write an expression $d(t)$ for the distance the car travels from $P$ .

Answer to Problem 44E

An expression $d(t)=45t$ for the distance the car travels from $P$ .

Explanation of Solution

Given information:

The speed of the car is given 45mph. Car starts at $t=0$ .

Speed is the change in distance traveled by the object with time .It can be represent as $\begin{array}{l}\frac{dx}{dt}=45\\ dx=45dt\end{array}$

Integrate the above equation:

  $x=45t+c$ …(1)

It is given that $t=0,x=0$ .

Substitute these values in equation (1);

  $\begin{array}{l}0=45\cdot 0+c\\ c=0\end{array}$

Substitute the value of $c$ equation (1) it gives;

  $x=45t$

This can be rewritten as $d(t)=45t$ .

(b)

To determine

To find: Find the graph of $d(t)=45t$ .

Answer to Problem 44E

The graph is given.

Explanation of Solution

Given information:

The function for distance traveled by car is given $d(t)=45t$ .

Starting from $t=0$ we draw the graph of the function $y=d\left(t\right)$

The graph of the function is given below:

  

(c)

To determine

To find: What is the slope of graph $y=45t$

Answer to Problem 44E

The slope is 45. This means that the distance is changing 45 meter per hour.

Explanation of Solution

Given information:

The function for distance traveled by car is given $d(t)=45t$ .

The graph is given :

  

Calculation:

Take any two points on the line.

Take $\left(2,90\right)$ and $\left(3,135\right)$ .

Apply the formula of slope $m=\frac{y_2-y_1}{x_2-x_1}$

Substitute $x_1=2,y_1=90,x_2=3,y_2=135$ .

  $\begin{array}{l}m=\frac{135-90}{3-2}\\ m=\frac{45}{1}\\ m=45\end{array}$

The slope is 45. This means that the distance is changing 45 meter per hour.

(d)

To determine

To find: Create a scenario for which $t$ could have negative values.

Answer to Problem 44E

Such scenario is not possible since time cannot be reduced.

Explanation of Solution

Given information:

The function for distance traveled by car is given $d(t)=45t$ .

If the car travels back in the opposite direction of where it was going before, Time cannot be negative. It can not be reduced.

(e)

To determine

To find: Create a scenario for which $y$ intercept is 30.

Answer to Problem 44E

The intercept $y$ will be 30 when time is 1.5.

Explanation of Solution

Given information:

It is given that the function for distance traveled by car is $y=45t$ and $y$ intercept is 30.

Substitute $y=30$ in the given equation:

  $\begin{array}{l}30=45t\\ t=\frac{45}{30}\\ t=\frac{3}{2}\\ t=1.5\end{array}$

The intercept $y$ will be 30 when time is 1.5.