A body of mass $1 \,kg$ is projected from ground at an angle $30^{\circ}$ with horizontal on a level ground at a speed $50 \,m / s$. The magnitude of change in momentum of the body during its flight is ....... $kg ms ^{-1}$ $\left(g=10 \,m / s ^2\right)$

Two seconds after projection a projectile is travelling in a direction inclined at $30^o$ to horizontal, after one more second it is travelling horizontally. What is the magnitude and direction of its velocity at initial point 

For a particle in uniform circular motion, the acceleration $\overrightarrow{ a }$ at any point $P ( R , \theta)$ on the circular path of radius $R$ is (when $\theta$ is measured from the positive $x\,-$axis and $v$ is uniform speed)

A projectile is thrown into space so as to have maximum horizontal range $R$. Taking the  point of projection as origin, the coordinates of the points where the speed of the  particle is minimum are-

A body slides down a frictionless track which ends in a circular loop of diameter $D$, then the minimum height $h$ of the body in term of $D$ so that it may just complete the loop, is

The $x-t$ graph of a particle moving along a straight line is shown in figure The distance-time graph of the particle is correctly shown by