A particle is going in a spiral path, as shown in figure with constant speed.

A circular road of radius $r$ is banked for a speed $v=40 \mathrm{km} {\mathrm{hr}}^{-1}.$ A car of mass $m$ attempts to go on the circular road. The friction coefficient between the tyre and the road is negligible.

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

(a) If the radial acceleration $\left(\mathrm{in} \mathrm{cm} {\mathrm{s}}^{-2}\right)$ of the particle at $t=1 \mathrm{s}$ is $\alpha$.

(b) If the tangential acceleration $\left(\mathrm{in} \mathrm{cm} {\mathrm{s}}^{-2}\right)$ at $t=1 \mathrm{s}$ is $\gamma$.

(c) If the magnitude of the acceleration$\left(\mathrm{in} \mathrm{cm} {\mathrm{s}}^{-2}\right)$  at $t=1 \mathrm{s}$ is $\sqrt{\beta }$ .

Then find $\alpha +\beta +\gamma$.