Chapter 7.1, Problem 17E

a.

To determine

To find: The position of the particle at the end of the trip.

Answer to Problem 17E

The position of the particle at the end of the trip is $6\text{ m}$ .

Explanation of Solution

Given information:

The graph of the velocity of the particle is given.

Calculation:

Observe that the velocity is always positive on the interval $\left[0,4\right]$ .

So, the displacement of the particle is sum of the areas under the curve on $\left[0,4\right]$ .

The area under each curve is the area of the triangle of height 2 m and base 1 m. The area of one triangle is $\frac{1}{2}\times \text{base}\times \text{height}=\frac{1}{2}\times 2\times 1=1{\text{ m}}^2$ .

So, $\text{Displacement}=4\times 1=4\text{ m}$ Displacement.

Therefore,

  $\begin{array}{c}\text{Final position}=\text{Initial position }+\text{ displacement}\\ =2+4\\ =6\text{ m}\end{array}$

Conclusion:

The position of the particle at the end of the trip is $6\text{ m}$ .

b.

To determine

To find: The total distance traveled by the particle.

Answer to Problem 17E

The total distance traveled by the particle is $4\text{ m}$ .

Explanation of Solution

Given information:

The graph of the velocity of the particle is given.

Calculation:

Observe that the velocity is always positive on the interval $\left[0,4\right]$ .

So, the total distance traveled by the particle is sum of the areas under the curve on $\left[0,4\right]$ .

The area under each curve is the area of the triangle of height 2 m and base 1 m. The area of one triangle is $\frac{1}{2}\times \text{base}\times \text{height}=\frac{1}{2}\times 2\times 1=1{\text{ m}}^2$ .

Therefore, the total distance traveled by the particle is $4\times 1=4\text{ m}$ .

Conclusion:

The total distance traveled by the particle is $4\text{ m}$ .