Consider the motion of the tip of the second hand of a clock. In one minute (assuming $R$ to be the length of the second hand), its:

Three girls skating on a circular ice ground of radius $200$ m start from a point $P$ on the edge of the ground and reach a point $Q$ diametrically opposite to $P$ following different paths as shown in the figure. The correct relationship among the magnitude of the displacement vector for three girls will be:

1. $A > B > C$
2. $C > A > B$
3. $B > A > C$
4. $A = B = C$

The position of a moving particle at time $t$ is $\overrightarrow{r}=3\hat{i}+4t^{2}\hat{j}-t^{3}\hat{k}.$ Its displacement during the time interval $t=1$ s to $t=3$ s will be:

A particle starting from the point $(1,2)$ moves in a straight line in the XY-plane. Its coordinates at a later time are $(2,3).$ The path of the particle makes with $x$-axis an angle of:

A particle starting from the origin $(0,0)$ moves in a straight line in the $(x,y)$ plane. Its coordinates at a later time are ($\sqrt{3}$, $3).$ The path of the particle makes an angle of __________ with the $x$-axis:
1. $30^\circ$
2. $45^\circ$
3. $60^\circ$
4. $0$

A cat is situated at point $A$ ($0,3,4$) and a rat is situated at point $B$ ($5,3,-8$). The cat is free to move but the rat is always at rest. The minimum distance travelled by the cat to catch the rat is:
1. $5$ unit
2. $12$ unit
3. $13$ unit
4. $17$ unit

Coordinates of a particle as a function of time $t$ are $x= 2t$,
$y =4t$. It can be inferred that the path of the particle will be:

An aeroplane flies $400$ m north and then $300$ m west and then flies $1200$ m upwards. Its net displacement is:

A particle is moving on a circular path of radius $R.$ When the particle moves from point $A$ to $B$ (angle $\theta$), the ratio of the distance to that of the magnitude of the displacement will be:

         
1. $\dfrac{\theta}{\sin\frac{\theta}{2}}$
2. $\dfrac{\theta}{2\sin\frac{\theta}{2}}$
3. $\dfrac{\theta}{2\cos\frac{\theta}{2}}$
4. $\dfrac{\theta}{\cos\frac{\theta}{2}}$