When t$=0$t$=0,$ the train has a speed of $88$ m$/$s$,$ which is increasing at $0\mathrm{.}5$ms$20\mathrm{.}5$ms$2.$

The radius of curvature of the tracks$$ at point AA is A$=400$A$=400$ m$.$

$$

Determine the magnitude of the acceleration of the engine when it reaches point AA$,$ at t$=20$t$=20$ s$.$