The kinetic energy $k$ of a particle moving along a circle of radius $R$ depends on the distance covered $s$ as $k = as^2$,where $a$ is a constant. The force acting on the particle is

$A$ particle is in uniform circular motion. The equation of its trajectory is given by $(x-2)^2+y^2=25$,where $x$ and $y$ are in meters. The speed of the particle is $2 \text{ m/s}$. When the particle attains the lowest $y$ coordinate,the acceleration of the particle is (in $\text{m/s}^2$):

$A$ car moves with a speed of $30 \, m/s$ on a circular path of radius $500 \, m$. If its tangential acceleration is $2 \, m/s^2$,what is the magnitude of the total acceleration of the car in $m/s^2$?

The angular velocity of a particle of a rigid body is not constant. Which of the following statements is true?

$A$ particle is moving in a circular path. The acceleration and momentum of the particle at a certain moment are $\vec a = (4\hat i + 3\hat j)\ m/s^2$ and $\vec p = (8\hat i - 6\hat j)\ kg \cdot m/s$. The motion of the particle is

In a circular motion of a particle,the tangential acceleration of the particle is given by $a_t = 12 \ m/s^2$. The radius of the circle is $3 \ m$. The particle was initially at rest. The time after which the total acceleration of the particle makes an angle $45^{\circ}$ with the radial acceleration is