A particle moves along an arc of a circle of radius $R$. Its velocity depends on the distance covered $s$ as $v=a\sqrt{s}$, where, $a$ is a constant. Then the angle between the vector of total acceleration and the vector of velocity as a function of $s$ will be?

A spotlight $S$ rotates in a horizontal plane with a constant angular velocity of $0.1 \mathrm{rad} {\mathrm{s}}^{-1}$. The spot of the light, $P$ moves along the wall at a distance $3 \mathrm{m}$. What is the velocity of the spot $P$ when $\text{θ}=45°$?

A particle $A$ moves along a circle of radius, $R=50 \mathrm{cm}$so that its radius vector $r$, relative to the point $O$ (figure), rotates with the constant angular velocity, $\omega =0.40 \mathrm{rad} {\mathrm{s}}^{-1}$. Then, the modulus of the velocity $\left(v\right)$ of the particle and the modulus of its total acceleration $\left(a\right)$ will be,