Find the following for path C in Figure 2.59:

(a) The distance travelled.

(b) The magnitude of the displacement from start to finish.

(c) The displacement from start to finish.

Thedistance is the total length of the path taken by the body. The meter is the measuring unit. It's a scalar value in the form of a number.

Displacement is the shortest distance between the starting and ending places.

It's a quantity with a vector attached to it. The length is expressed in the meter.

Only if the journey is a straight line will the distance and displacement be the same.

Path of particle C

a. The distance traveled by particle C is:

First, it goes from$\mathbf{x}=\mathbf{2}\mathbf{m}\mathbf{to}\mathbf{x}=\mathbf{10}\mathbf{m}$ . The total distance covered isrole="math" localid="1655548998848" $\mathbf{8}\mathbf{meters}$ . Then the body comes back till $\mathbf{8}\mathbf{meters}$, so it covers more distance. Now the total distance will be $\mathbf{8}+\mathbf{2}=\mathbf{10}\mathbf{meter}$. Again, the body goes from $\mathbf{x}\mathbf{=}\mathbf{\text{8}}\mathbf{m}\mathbf{to}\mathbf{x}\mathbf{=}\mathbf{10}\mathbf{m}$. Here it covers $\mathbf{2}\mathbf{meters}$. So, the final distance traveled by the body is $\mathbf{10}+\mathbf{2}=\mathbf{12}\mathbf{meter}$.

The distance covered by particle C is $\mathbf{12}\mathbf{meters}$.

Displacement of the particle C = Final position– Initial Position

$\begin{array}{l}=\mathbf{10}\mathbf{meters}–\mathbf{2}\mathbf{meters}\\ =\mathbf{8}\mathbf{meters}\end{array}$