$A$ particle is moving eastwards with a velocity of $5\,m/s$. In $10\,s$,the velocity changes to $5\,m/s$ northwards. The average acceleration in this time 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

Two bodies of masses $m$ and $3m$ are rotating in horizontal circles of radii $r$ and $\frac{r}{3}$ respectively. The tangential speed of the body of mass $m$ is $n$ times that of the heavier body. If the centripetal force is the same for both,the value of $n$ is:

$A$ particle of mass $m$ is moving in the $xy$-plane such that its velocity at a point $(x, y)$ is given as $\vec{v} = \alpha(y \hat{i} + 2x \hat{j})$,where $\alpha$ is a non-zero constant. What is the force $\vec{F}$ acting on the particle?

$A$ cricketer can throw a ball to a maximum horizontal distance of $100\,m$. With the same speed,how high above the ground can the cricketer throw the same ball (in $,m$)?

Two stones of masses $m$ and $2\,m$ are whirled in horizontal circles,the heavier one in a radius $\frac{r}{2}$ and the lighter one in radius $r$. The tangential speed of the lighter stone is $n$ times that of the heavier stone when they experience the same centripetal force. The value of $n$ is