$A$ particle is moving with a constant speed of $\sqrt{2} \, m/s$ on a circular path of radius $10 \, cm$. Find the magnitude of the average velocity when it has covered $\frac{3}{4}$ of the circular path.

Three point particles $P, Q, R$ move in a circle of radius $r$ with different but constant speeds. They start moving at $t = 0$ from their initial positions as shown in the figure. The angular velocities (in $\text{rad/s}$) of $P, Q$ and $R$ are $5\pi, 2\pi$ and $3\pi$ respectively,in the same sense. The number of times $P$ and $Q$ meet in the time interval $t = 0$ to $t = 1 \text{ s}$ is:

$A$ ball is thrown up with a certain velocity at an angle $\theta$ to the horizontal. The kinetic energy $KE$ of the ball varies with horizontal displacement $x$ as

The diameter of a car wheel is $60 \ cm$. How many radians of angular displacement will the wheel have undergone while the car travels a distance of $1.2 \ km$?

$A$ projectile is fired at an angle of $30^{\circ}$ to the horizontal such that the vertical component of its initial velocity is $80\,m/s$. Its time of flight is $T$. Its velocity at $t=\frac{T}{4}$ has a magnitude of nearly $........\,m/s$.

$A$ 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?