If the equation for the angular displacement of a particle moving on a circular path is given by $\left(\mathrm{\theta }\right) = 2t^3 + 0.5$, where $\mathrm{\theta }$ is in radians and $t$ in seconds, then find the angular velocity of the particle after $2 \mathrm{seconds}$ from its start.

A particle moves in a circle of radius $1.0 \mathrm{cm}$ at a speed given by $v=2.0t$ where $v$ is in $\mathrm{cm} {\mathrm{s}}^{-1}$ and $t$ in seconds.

(a) Find the radial acceleration of the particle at $t=1 \mathrm{s}$.

(b) Find the tangential acceleration at $t=1 \mathrm{s}$.

(c) Find the magnitude of the acceleration at $t=1 \mathrm{s}$.