Problem 1.38

A point moves with deceleration along the circle of radius $R$ so that at any moment of time its tangential and normal accelerations are equal in moduli. At the initial moment $t=0$ the velocity of the point equals $v_{0} .$ Find: (a) the velocity of the point as a function of time and as a function of the distance covered $s$ ; (b) the total acceleration of the point as a function of velocity and the distance covered.

\text { (a) } v=v_{0} /\left(1+v_{0} t / R\right)=v_{n} \mathrm{e}^{-z / R} \text { (b) } w=\sqrt{\overline{2}} v_{0}^{2} / R \mathrm{e}^{2 s / R}= =\sqrt{\overline{2}} v^{2} / R

Kinematics