(a) Forces $F_1=\left(\begin{array}{cc}-5& 4\end{array}\right)N;F_2=\left(\begin{array}{c}2\\ 5\end{array}\right)N;F_3=\left(\begin{array}{cc}2& -1\end{array}\right)N$ and $F_4=\left(\begin{array}{cc}3& -5\end{array}\right)N$ act on a body. Find the :
(i) resultant of these forces ; (ii) fifth force that will keep the body in equilibrium.
(b) A body moving at 20 ms${}^{-1}$ accelerates uniformly at 2.5 ms${}^{-2}$ for 4 seconds. It continues the journey at the speed for 8 seconds, before coming to rest in t seconds with a uniform retardation. If the ratio of the acceleration to the retardation is 3 : 4,
(i) sketch the velocity- time graph of the journey ; (ii) find t ; (iii) find the total distance of the journey.


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