$A$ particle moves towards east with a velocity of $5\ m/s$. After $10\ s$,its direction changes towards north with the same velocity. The average acceleration of the particle is:

The second's hand of a watch has $6\, cm$ length. The speed of its tip and the magnitude of the difference in velocities of its tip at any two perpendicular positions will be respectively:

Two particles $A$ and $B$ are projected simultaneously in the directions shown in the figure with velocities $V_A = 20 \ ms^{-1}$ and $V_B = 10 \ ms^{-1}$ respectively. They collide in the air after $0.5 \ s$. Find $(a)$ the angle $\theta$ and $(b)$ the distance $x$.

At $t = 0$,a projectile is fired from a point $O$ (taken as origin) on the ground with a speed of $50 \, m/s$ at an angle of $53^{\circ}$ with the horizontal. It passes through two points $A$ and $B$,each at a height of $75 \, m$ above the horizontal,as shown in the figure. Find the distance (in meters) of the particle from the origin at $t = 2 \, s$.

Consider a circle of radius $R = 42\ cm$. An insect crawls with a uniform speed of $v = 1.3\ cm/s$ along the chord $AB$, then along the circular arc $BCD$, and finally along the chord $DA$ to return to point $A$. The time taken by the insect to crawl from $A$ back to $A$ is closest to ......... $\sec$.

Three point particles $P, Q, R$ move in a circle of radius $r$ with different but constant speeds. They start moving at $t = 0$ from their initial positions as shown in the figure. The angular velocities (in $\text{rad/s}$) of $P, Q$ and $R$ are $5\pi, 2\pi$ and $3\pi$ respectively,in the same sense. The number of times $P$ and $Q$ meet in the time interval $t = 0$ to $t = 1 \text{ s}$ is: