Question

Find the following for path B 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) 4 m.

b) 4.

c) -4 m.

Step-by-step solution

Distance and displacement

The entire length of the path traveled by the body is the distance. The meter is the unit of measurement. It's a number with a scalar value.

The smallest distance between the initial and end positions is defined as displacement.

It's a quantity with a vector. It is measured in meters.

If the path is a straight line, the distance and displacement will be the same only in such a case.

For particle B distance and displacement

Path of particle B

a. The distance traveled by the particle B is:

$$\begin{gathered} \mathbf{=}\mathbf{12}\mathbf{meter}\mathbf{-}\mathbf{8}\mathbf{meter}\mathbf{.} \\ \mathbf{=}\mathbf{\text{4\hspace{0.17em}meter}} \end{gathered}$$

The distance covered by particle B is $\mathbf{4}\mathbf{meter}$.

b. The magnitude of the displacement, in this case, will be the same as the distance as it is a straight path which is role="math" localid="1655548082697" $\mathbf{4}\mathbf{meter}$

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