$A$ particle moves once around a circle of radius $1 \,m$. The time taken is $10 \,s$. The average velocity of the motion is

For a given initial velocity,a projectile is fired at angles of $30^\circ$ and $60^\circ$. Find the ratio of their maximum heights.

$A$ strap is passing over a wheel of radius $30\, cm.$ During the time the wheel moving with an initial constant velocity of $2\, rev/s$ comes to rest,the strap covers a distance of $25\, m.$ The deceleration of the wheel in $rad/s^2$ is

$A$ projectile is thrown upward with a velocity $v_0$ at an angle $\alpha$ to the horizontal. The change in velocity of the projectile when it strikes the same horizontal plane is

Three particles start simultaneously from a point on a horizontal smooth plane. The first particle moves with speed $v_1$ towards the east,the second particle moves towards the north with speed $v_2$,and the third one moves towards the north-east. The velocity of the third particle,such that the three particles always lie on a straight line,is

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 ......... $\sec$.