$A$ 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

$A$ boy throws a ball with a velocity $V_0$ at an angle $\alpha$ to the ground. At the same time,he starts running with a uniform velocity to catch the ball before it hits the ground. To achieve this,he should run with a velocity of

$A$ 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:

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 $x$.

$A$ projectile crosses two walls of equal height $H$ symmetrically as shown in the figure. The time of flight $T$ is given by ........ $\text{s}$.

The coordinates of a moving particle at any time $t$ are given by $x = \alpha t^3$ and $y = \beta t^3$,where $\alpha$ and $\beta$ are constants. The speed of the particle at time $t$ is given by: