$A$ particle is moving in a circle with uniform speed '$v$'. In moving from a point to another diametrically opposite point:

$A$ 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 position coordinates of a projectile projected from the ground on a certain planet (with no atmosphere) are given by $y = (4t - 2t^2) \text{ m}$ and $x = (3t) \text{ m}$,where $t$ is in seconds and the point of projection is taken as the origin. The angle of projection of the projectile with the vertical is ......... (in $^{\circ}$)

$A$ man wants to reach from $A$ to the opposite corner of the square $C$. The sides of the square are $100\, m$. $A$ central square of $50\, m \times 50\, m$ is filled with sand. Outside this square,he can walk at a speed of $1\, m/s$. In the central square,he can walk only at a speed of $v\, m/s$ $(v < 1)$. What is the smallest value of $v$ for which he can reach faster via a straight path through the sand than any path in the square outside the sand?

The coordinates of a moving particle at any time $t$ are given by $x = a\, t^2$ and $y = b\, t^2$. The speed of the particle is

$A$ ball is thrown up with a certain velocity at an angle $\theta$ to the horizontal. The kinetic energy $KE$ of the ball varies with horizontal displacement $x$ as