Q3PE - College Physics (Urone)

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.

Step-by-Step Solution

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 1: Distance and displacement

The distance 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.

Step 2: 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 is  $\mathbf{8}\mathbf{meters}$ . 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.