$A$ point moves in the $x-y$ plane according to the law $x = 3 \cos 4t$ and $y = 3(1 - \sin 4t)$. The distance travelled by the particle in $2 \text{ s}$ is...........$m$ (where $x$ and $y$ are in meters).

$A$ racing car is moving with velocity $v = 40\ m/s$ on a straight track as shown. We are recording it with a camera placed at a distance of $30\ m$ from the road. Find the angular velocity (in $rad/s$) with which we should rotate the camera to record the race at the instant shown in the diagram.

$A$ block of mass $5 \, kg$ is moving with a horizontal velocity of $1.5 \, m/s$. $A$ force of $5 \, N$ is applied in the perpendicular (vertical) direction for $4 \, s$. The total distance covered by the block is .......... $m$.

$A$ $2 \ kg$ ball is thrown vertically upward and another $3 \ kg$ ball is projected with a certain angle $(\theta \neq 90^{\circ})$. Both have the same time of flight. The ratio of their maximum heights is:

$A$ particle is in uniform circular motion. Its velocity is perpendicular to which of the following?

$A$ ring of mass $m$ moves from point $1$ to point $2$ along a smooth rigid horizontal wire with a constant speed $v$. The average force acting on the ring over the time of its motion from $1$ to $2$ is