$A$ particle is moving in a circle of radius $R$ with constant speed $V$. The magnitude of average acceleration after half revolution is

Starting from the origin at time $t=0,$ with initial velocity $5 \hat{j} \, m/s,$ a particle moves in the $x-y$ plane with a constant acceleration of $(10 \hat{i} + 4 \hat{j}) \, m/s^2$. At time $t$,its coordinates are $(20 \, m, y_0 \, m)$. The values of $t$ and $y_0$ are respectively:

$A$ shot is fired from a point at a distance of $200 \ m$ from the foot of a tower $100 \ m$ high,such that it just passes over it. The direction of the shot with respect to the horizontal is (in $^{\circ}$)

$A$ body of mass $1\,kg$ is projected with velocity $50\,m/s$ at an angle of $30^{\circ}$ with the horizontal. At the highest point of its path,a force of $10\,N$ starts acting on the body for $5\,s$ vertically upward in addition to the gravitational force. What is the horizontal range of the body? $\left(g=10\,m/s^2\right)$

$A$ body is moving with constant speed in a circle of radius $10 \ m$. The body completes one revolution in $4 \ s$. At the end of the $3^{rd}$ second,the displacement of the body (in $m$) from its starting point is:

$A$ particle moves in the $xy$ plane according to the law $x = a \sin \omega t$ and $y = a(1 - \cos \omega t)$,where $a$ and $\omega$ are constants. The particle traces: