Chapter 2.1, Problem 5R

To determine

To describe: The trip from home to school in terms of displacement, distance, position and speed.

Explanation of Solution

Introduction:

Position: It tells about the location of object with respect to some reference point.

Displacement: It is defined as change in position of object. It is a vector quantity.

  $\Delta x=x_f-x_i$

The S.I unit of displacement is meter (m).

Distance: It is the total distance travelled by object. It is a scaler quantity.

Speed: It is defined as rate of change of distance.

  $v=\frac{D}{t}$

Where,

  $v$ = speed

  $D$ = distance

  $t$ = time

Velocity: It is defined as rate of change of displacement. It is a vector quantity.

  $\overrightarrow{v}=\frac{\overrightarrow{d}}{t}$

Where,

  $\overrightarrow{v}$ = velocity

  $\overrightarrow{d}$ = distance

  $t$ = time

Consider point $A$ is the position of home and $B$ is the position of home. The distance between the home and school is $x$ . The time taken by a boy to go from home to school is $t$ .

Distance: The total distance covered by the boy is $2x$ .

Displacement: It is the difference between initial and final point. The final position of boy is same because boy is returned back to home.

So, displacement is zero.

  $\overrightarrow{d}=0$

Speed: It is the ratio of net distance covered by body to time taken. So the speed of boy is,

  $\begin{array}{l}v=\frac{2x}{2t}\\ v=\frac{x}{t}\end{array}$

Velocity: It is the ratio of net displacement of body to time taken. So the displacement of body is,

  $\begin{array}{l}\overrightarrow{v}=\frac{0}{2t}\\ \overrightarrow{v}=0\end{array}$