$A$ train is moving at a speed of $50\, m s^{-1}$ on a curved track of radius $250\, m$. What is its acceleration (in $, m s^{-2}$)?

$A$ particle moves in a circle with speed $v$ varying with time as $v(t) = 2t$. The total acceleration of the particle after it completes $2$ rounds of the cycle is:

For circular motion,if $\vec a_t$,$\vec a_c$,$\vec r$ and $\vec v$ are tangential acceleration,centripetal acceleration,radius vector and velocity respectively,then find the wrong relation.

$A$ 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

$A$ car is moving with speed $30 \,m/s$ on a circular path of radius $500 \,m$. Its speed is increasing at a rate of $2 \,m/s^2$. What is the total acceleration of the car (in $\,m/s^2$)?

If $\theta$ is the angle between the velocity vector $\vec{v}$ and the acceleration vector $\vec{a}$ of a particle moving on a circular path with decreasing speed,then .........