Question: Figure $1$ shows the displacement along the $x$ axis vs time for a cart. The cart starts from rest at the origin at $t=0.$ From $0t_A$ the graph is parabolic. For this graph $t_A=6\mathrm{.}92s,t_B=13\mathrm{.}84s,x_A=12\mathrm{.}4m$ and $x_B=22\mathrm{.}3m.$ Give your answer with the correct number of significant figures. Figure $1$: A displacement$-$time graph representing the movement of the described cart. A parabolic curve connects the origin to the point $(t_A,x_A)$ and a diagonal line connects this point to the point $(t_B,x_B).$ Part $1)$ Write an expression for the velocity in the $x$ direction for the times $v_x=$hat$(i)\frac{m}{s}0s.$ Simplify and evaluate your expression $as$ much $as$ possible. $v_{?}$