$A$ particle moves with a constant speed of $5 \, ms^{-1}$ as shown in the figure. What is the change in velocity during half a revolution in $ms^{-1}$?

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:

The maximum range of a bullet fired from a toy pistol mounted on a car at rest is $R_0 = 10 \, m$. What will be the acute angle of inclination of the pistol for maximum range when the car is moving in the direction of firing with uniform velocity $v = 20 \, m/s$,on a horizontal surface? $(g = 10 \, m/s^2)$

Two particles are projected simultaneously in the same vertical plane,from the same point on the ground,with the same speeds but at different angles $( < 90^o )$ to the horizontal. The path followed by one,as seen by the other,is

$A$ car travels north with a uniform velocity. It goes over a piece of mud which sticks to the tyre. The particles of the mud,as they leave the ground,are thrown:

$A$ particle is projected with a velocity $v$ such that its range on the horizontal plane is twice the greatest height attained by it. The range of the projectile is ($g=$ acceleration due to gravity).