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

$A$ particle is projected from the ground with some initial velocity making an angle of $45^{\circ}$ with the horizontal. If it reaches a height of $7.5 \ m$ above the ground,while it travels a horizontal distance of $10 \ m$ from the point of projection,then the initial speed of the particle is (assume,$g=10 \ m/s^2$): (in $m/s$)

$A$ car starts from rest and accelerates at $5 \, m/s^{2}$. At $t=4 \, s$,a ball is dropped out of a window by a person sitting in the car. What is the velocity and acceleration of the ball at $t=6 \, s$? (Take $g = 10 \, m/s^{2}$)

Two bodies of mass $10 \ kg$ and $5 \ kg$ are moving in concentric circular orbits of radii $R$ and $r$ respectively such that their periods are same. The ratio between their centripetal acceleration is

$A$ particle is moving in the $xy$-plane and crosses the origin at time $t=0$. The equation of motion of the particle is $y=4x^2$. If the velocity of the particle is $\vec{v}=(2\hat{i}+2\hat{j}) \text{ m s}^{-1}$ and acceleration is $\vec{a}=(a\hat{j}) \text{ m s}^{-2}$,then the magnitude of $a$ is

$A$ body of mass $m$ is projected at an angle of $45^{\circ}$ with the horizontal with an initial velocity $v$. If air resistance is negligible,then the total change in momentum when it strikes the ground is: