Question

Find the following for path D 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

a) 8 m

b) 4 m

c) -4 m

Step-by-step solution

Distance and displacement

The distance is the whole length of the body's journey. The meter is the unit of measurement. It's a number that represents a scalar value.

The shortest distance between the beginning and finishing points is defined as displacement. It's a quantity that's been given a vector. The length is given in meters.

The distance and displacement will be the same only if the voyage is in a straight line.

For particle D distance and displacement

Figure: Path of particle D

a. The distance travelled by the particle D is :

First, it goes from$\mathbf{x}=\mathbf{9}\mathbf{m}\mathbf{to}\mathbf{x}=\mathbf{3}\mathbf{m}$. The total distance covered is $\mathbf{6}\mathbf{m}$. Then the body comes back till $\mathbf{5}\mathbf{}\mathbf{m}$, so it covers more distance. Now the total distance will be $\text{6+}2=\text{8\hspace{0.17em}m}$.

Thus, the distance covered by particle D is $\mathbf{8}\mathbf{m}$.

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 D =Final position – Initial Position

$\begin{array}{l}\mathbf{\text{=5\hspace{0.17em}m}}\mathbf{-}\mathbf{\text{9\hspace{0.17em}m}}\\ \mathbf{\text{=}}\mathbf{-}\mathbf{\text{4\hspace{0.17em}m}}\end{array}$

Thus, the magnitude will be 4 m.

c. The direction of the displacement would be $\mathbf{-}\mathbf{4}\mathbf{m}$as the body is moving in the negative x-direction.