Question

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.

Short answer

The path of C is not a straight line, so distance and displacement will be of different values.

1. 12 m
2. 8
3. +8 m

Step-by-step solution

Distance and displacement

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.

Distance and displacement for particle C

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 $\mathbf{12}\mathbf{meters}$.

b. The magnitude of the displacement, in this case, will not be the same as the distance as it is not a straight path.

Displacement of the particle C = Final position– Initial Position

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

c. The direction of the displacement would be $+\mathbf{8}\mathbf{m}$as the body moves in the positive x-direction.