1   An object has moved through a distance. Can it have zero displacement? If yes, support your answer with an example.

Solution :

Yes. An object that has moved through a distance can have zero displacement. Displacement is the shortest measurable distance between the initial and the final position of an object. An object which has covered a distance can have zero displacement, if it comes back to its starting point, i.e., its initial position. Consider the following situation. A man is walking in a square park of length $20 m$ (as shown in the following figure). He starts walking from point A and after moving along all the corners of the park (point $B, C, D$), he again comes back to the same point, i.e., A.$\\$ In this case, the total distance covered by the man is $20 m + 20 m + 20 m + 20 m = 80 m.$ However, his displacement is zero because the shortest distance between his initial and final position is zero.

2   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 :

The farmer takes $40 $s to cover $4 × 10 = 40 m.$$\\$ In $2$ min and $20$ s ($140$ s), he will cover a distance= $\dfrac{40}{40}*140=140 m$$\\$ Therefore, the farmer completes $\dfrac{140}{40}=3.5$ rounds(3complete rounds and a half round ) of the field in $2$ min and $20$ s.$\\$ That means, after $2$ min $20$ s, the farmer will be at the opposite end of the starting point.$\\$ Now, there can be two extreme cases.$\\$ $\text{Case I:}$ Starting point is a corner point of the field.$\\$ In this case, the farmer will be at the diagonally opposite corner of the field after $2$ min $20$ s.$\\$ Therefore, the displacement will be equal to the diagonal of the field.$\\$ Hence, the displacement will be $\sqrt{10^2 +10^2 }= 14.1 m$$\\$ $\text{Case II:}$ Starting point is the middle point of any side of the field.$\\$ In this case the farmer will be at the middle point of the opposite side of the field after $2$ min $20$ s.$\\$ Therefore, the displacement will be equal to the side of the field, i.e., $10$ m.$\\$ For any other starting point, the displacement will be between $14.1 m $ and $10 m.$

3   Which of the following is true for displacement?$\\$ (a) It cannot be zero.$\\$ (b) Its magnitude is greater than the distance travelled by the object.

Solution :

(a) Not true$\\$ Displacement can become zero when the initial and final position of the object is the same.$\\$ (b) Not true$\\$ Displacement is the shortest measurable distance between the initial and final positions of an object. It cannot be greater than the magnitude of the distance travelled by an object. However, sometimes, it may be equal to the distance travelled by the object.

4   An artificial satellite is moving in a circular orbit of radius $42250 km$. Calculate its speed if it takes $24$ hours to revolve around the earth?

Solution :

Radius of the circular orbit, $r = 42250 km$$\\$ Time taken to revolve around the earth,$ t = 24 h$$\\$ Speed of a circular moving object,$v=\dfrac{2 \pi r}{t}$$\\$ $=\dfrac{2*3.14*42250}{24}\\ =1.105*10^4 km/h\\ =3.069 km /s$$\\$ Hence, the speed of the artificial satellite is $3.069 km/s.$

5   Distinguish between speed and velocity.

Solution :

$\textbf{Speed}$ $\to$ Speed is the distance travelled by an object in a given interval of time. It does not have any direction.$\\$ $\to$ Speed is given by the relation:$\\$ Speed=\dfrac{\text{Distance travelled}}{\text{Time taken}}$\\$ $\to$ The speed of an object can never be negative. At the most, it can become zero. This is because distance travelled can never be negative.$\\$ $\textbf{Velocity }$$\\$ $\to$ Velocity is the displacement of an object in a given interval of time. It has a unique direction.$\\$ $\to $ Velocity is given by the relation:$\\$ Velocity=\dfrac{\text{Displacement}}{\text{Time interval}}$\\$ $\to$ The velocity of an object can be negative, positive, or equal to zero. This is because displacement can take any of these three values.