Chapter 8.8, Problem 27E

To determine

To Find: The distance travelled by the car in the next round and if it is reasonable to use the polynomial to estimate the distance travelled during the next time.

Answer to Problem 27E

The distance travelled by the car in the next round is $21\text{m}$ time $T_2\left(t\right)$ is not accurate over the full minute as the acceleration is not constant that is $2\text{m}/{\text{s}}^2$ .

Explanation of Solution

Given:

The speed of the car is $20$ metre per second and the acceleration is $2\text{m}/{\text{s}}^2$ .

Calculation:

Consider the position of the car is $s\left(t\right)$ , then the velocity $V\left(t\right)=S^{\prime }\left(t\right)$ and acceleration $a\left(t\right)=S^{″}\left(t\right)$ .

The second degree polynomial is,

  $s\left(t\right)=T_2\left(t\right)+S\left(0\right)+V\left(0\right)t+\frac{a\left(0\right)}{2!}{t}^2$

From the given data,

  $V\left(0\right)=20\text{m}/\text{s}$

Also,

  $a\left(0\right)=2\text{m}/{\text{s}}^2$

Then,

  $S\left(t\right)=20t+t^2$

Then, the position of the car in the next second is obtained as,

  $\begin{array}{c}S\left(1\right)=20\left(0\right)+1^2\\ =21\text{m}\end{array}$

Thus, the time $T_2\left(t\right)$ is not accurate over the full minute as the acceleration is not constant that is $2\text{m}/{\text{s}}^2$ .