Chapter 14.3, Problem 13PPS

To determine

To calculate how much farther does the second car go.

Answer to Problem 13PPS

The second car goes 300 meters farther.

Explanation of Solution

Given information:

Car 1 travels $2t+t^2$ meters,

Car2 travels $2t-2t^2$ meters, where “t” is time in seconds.

Time is 10 seconds

Formula used: Polynomial subtraction

Calculation:

How much more did car 2 travel= Car 2’s distance- Car 1’s difference

Substituting the expressions,

  $=(2t+2t^2)-(2t-t^2)$

Opening the brackets,

  $=2t+2t^2-2t+t^2$

Re-arranging the expression,

  $\begin{array}{l}=2t-2t+2t^2+t^2\\ =3t^2\end{array}$

When, $t=10\sec$ :

Substituting the value of $t$ ,

  $\begin{array}{l}$ =3\times {(10)}^2$=3\times 100\\ =300\end{array}$

Hence, Car 2 goes 300 meters farther.