$A$ 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 $g = 10 \, m/s^{2}$)

$A$ frictionless circular wire of unit radius is fixed on the horizontal plane. Two point particles of unit mass start moving simultaneously from point $A(\theta = \pi/2)$ with identical uniform angular speeds in opposite directions, and meet again at point $B(\theta = -\pi/2)$. During this time, which of the following figures schematically represent the magnitude of the total linear momentum $P$ of the system, as a function of $\theta$?

$A$ small boy is throwing a ball towards a wall $6 \,m$ in front of him. He releases the ball at a height of $1.4 \,m$ from the ground. The ball bounces from the wall at a height of $3 \,m$,rebounds from the ground and reaches the boy's hand exactly at the point of release. Assuming the two bounces (one from the wall and the other from the ground) to be perfectly elastic,how far ahead of the boy did the ball bounce from the ground (in $,m$)?

$A$ particle is projected from a point at an angle $\theta$ with the horizontal direction. At any time $t$, if $p$ is the linear momentum, $y$ is the vertical displacement, and $x$ is the horizontal displacement, which of the following graphs does not represent the variation of kinetic energy $KE$ of the particle?

$A$ 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? $\left(g=10\,m/s^2\right)$

$A$ projectile is thrown with velocity $v$ making an angle $\theta$ with the vertical. It reaches a maximum height $H$. The time of flight is: