$[$Problems $1$ through $18]$ The below figure shows a roller$-$coaster ride. A small cartwith mass being $200$ kg is initially located at position O$.$ The cart is then elevated toposition A by a conveyor belt with a constant speed of$2$ m$/$s and comes to a stop. It isthen released with a negligible speed and falls down along the track, passing positions B$,$ C$,$D$,$ and E$.$ After passing E$,$ it reaches the maximum height and comes back to the initialposition O$.$ From position O to position T$,$ a non$-$zero friction is applied to stop the cart atT. Assume that no friction or air resistance works over the entire roller$-$coaster track exceptfor the region between O and T and the gravitational acceleration g is $9\mathrm{.}81$ m$/$s$2.$OABCDET