Question

A particle moved $5m$ towards the east and then moved $8m$ towards the west. What is the total distance traveled and the magnitude of displacement?

Answer 1

Step 1: Given data

1. Distance traveled by the particle in the east direction, $d_1=5m$
2. Distance traveled by the particle in the west direction, $d_2=8m$
3. The diagrammatic representation of the given data is given below:

Step 2: Find the total distance traveled by the particle

Distance:

1. The complete length of the path traveled to reach the destination.
2. It is a scalar quantity as it depends upon the magnitude and not the direction.
3. It can have positive values.

Displacement:

1. It is the shortest path between the initial and final positions.
2. It is a vector quantity as it has a direction and magnitude.
3. It can be positive, negative, and even zero.

Total distance traveled, $d=d_1+d_2$

$$\begin{gathered} =5+8 \\ =13m \end{gathered}$$

Step 3: Find the total displacement of the particle

Total displacement, $D=d_2-d_1$

$$\begin{gathered} =8-5 \\ =3m \end{gathered}$$

Thus, the total distance traveled by the particle is $\mathbf{13}\mathbf{}\mathit{m}$ and the magnitude of displacement is $\mathbf{3}\mathbf{}\mathit{m}$.