Chapter 8.1, Problem 17E

a.

To determine

To find where the particle is at the end of the trip.

Answer to Problem 17E

The Position of the particle at the end of the trip is 6.

Explanation of Solution

Given information:

The particle is moving on x-axis and starts at $x=2$ when $t=0$ .

Calculation:

Position of the particle at $\left(t=4\right)$ $=$ position at $\left(t=0\right)$ $+$ displacement from $\left(t=0\right)$ to $\left(t=4\right)$

  $\begin{array}{l}\text{position at}\left(t=4\right)=2+4\cdot \frac{1}{2}\cdot 2\cdot 1\left[\text{displacement}=\text{area under }v-t\text{ curve}\right]\\ =2+4\\ =6\end{array}$

Therefore,

The Position of the particle at the end of the trip is 6

b.

To determine

To find the total distance travelled at the end of the trip.

Answer to Problem 17E

Total distance travelled at the end of the trip is 4 meter.

Explanation of Solution

Given information:

The particle is moving on x-axis and starts at $x=2$ when $t=0$ .

Calculation:

Total distance travelled is equals to area under velocity time curve.

  $\begin{array}{l}S=4\cdot \frac{1}{2}\cdot 2\cdot 1\\ =4\end{array}$

Therefore,

Total distance travelled is 4 meter.