# Physics 9th: Motion | Distance and Displacement

## 9th Physics | Motion | Distance and Displacement

### Distance

(a)    The distance travelled by a body is the actual length of the path covered by a moving body irrespective of the direction in which the body travels

(b)    It is a scalar quantity therefore it has only magnitude

### Displacement

When a body moves from one point to another, the shortest distance between the initial position and final position of the body, along with direction, is known as displacement.

It is vector quantity therefore it has magnitude as well as direction.

Distance travelled by a moving body cannot be zero but the displacement of a moving body can be zero.

With increase in time distance can not decrease but displacement can.

### Some Solved Questions Based on Distance and Displacement

#### (c)    ABCDA

Solution:

(a)    Distance travelled from A to B = 10 m

Displacement from A to B = 10 m

Therefore distance and displacement are equal if     the object travels in the same straight path

(b)    Distance travelled from A to C = AB + BC

= 10 + 10

= 20 m

Displacement from A to C     = AC = $\displaystyle 10\sqrt{2}$    m.

Therefore distance travelled is always more than the displacement if there is a change in direction of motion

(c)    Distance travelled from A, back to A = AB + BC + CD + DA

= 10 + 10 + 10 + 10 = 40 m

Displacement from A, back to A = 0 m

This is because the shortest distance between initial position (A) and final position     (A) is zero.

Therefore the displacement of a moving object may be zero but distance travelled cannot be zero.

#### Question:     Calculate the distance and displacement of a body moving in a complete circle.

Solution:

If we take a round trip and reach back at the starting point, then although we have travelled some distance, our final displacement will be zero. This is because the straight line distance between initial and final position is zero

#### Question:     A farmer moves along the boundary of a square field of side 10 m in 40 s. What will be the magnitude of displacement of the farmer at the end of 2 minutes 20 seconds?

Solution:

In figure ABCD is a square field of side 10 m.

Time for one round = 40 s

Total time = 2 min 20 s

= (2 ´ 60 + 20) s

= 140 s

Number of rounds completed $\displaystyle =\frac{140}{40}=3.5$

If framer starts from A, it will complete 3 rounds $\displaystyle \left( A\to B\to C\to D\to A \right)$ at A. In the last 0.5 round starting from A, he will finish at C

\ Displacement $\displaystyle =AC$, where $\displaystyle AC=\sqrt{A{{B}^{2}}+B{{C}^{2}}}=\sqrt{{{10}^{2}}+{{10}^{2}}}=10\sqrt{2}$m

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