An automobile $P$ is traveling along a circular track of radius $R=958\mathrm{.}4m.$ At position $"$A$"$ on the track, the automobile has a speed of $v_A=10\mathrm{.}3$

$\frac{m}{s}.$ At this position, the driver of the automobile applies the brakes causing the speed of the automobile to change with distance $s$ traveled along

the track according to the following equation: $v(s)=v_{A}cos(0\mathrm{.}001s)\frac{m}{s}($cos is in radians$),$ where $s$ is given in meters.

Determine the magnitude of the acceleration for the driver when the automobile reaches position $"$B$"$ on the track where $"$B$"$ is a quarter of the

distance around the track from position $"$A$".$