Question

A book is moved once around the perimeter of a tabletop with the dimensions $\mathbf{1}\mathbf{.}\mathbf{0}\mathbf{}\mathbf{\text{m}}$by $\mathbf{2}\mathbf{.}\mathbf{0}\mathbf{}\mathbf{\text{m}}$.The book ends up at its initial position.

(a) What is its displacement?

(b) What is the distance travelled?

Short answer

(a) The displacement is zero.

(b) The distance travelled by the book is$6m$ .

Step-by-step solution

Define the displacement

It's a vector quantity with a magnitude and a direction. It's depicted as an arrow pointing from the beginning place to the destination.

For instance, if an object moves from position$\mathit{A}$ to $\mathit{B}$, its position changes. Displacement is the term for a shift in an object's position.

(a) Determining the displacement

The difference between a particle's final and starting position vectors is now defined as the particle's displacement vector$\Delta \overrightarrow{r}$ .

$\Delta \overrightarrow{r}={\overrightarrow{r}}_f-{\overrightarrow{r}}_i$

Here the book is moved once around the perimeter of a tabletop.

So in this case, both initial position and final position of the book on the tabletop are same.

Therefore, the displacement is zero.

(b) Determining the distance

The total distance travelled is equal to the tabletop's perimeter.

The tabletop's perimeter is given by,

$P=2(l+b)$

Here $P$is the perimeter of the tabletop, $l$is the length of the tabletop and is the width of the tabletop.

Substitute $0.1m$for$l$ and $2.0 \text{m}$for $b$in the above equation.

$$\begin{gathered} P=2(1+2) \text{m} \\ =6 m \end{gathered}$$

Therefore, the total distance travelled is $6m$.