Answer
$$v_{0}=6.0 \mathrm{m} / \mathrm{s}$$
$$and $$
$$a=2.0 \mathrm{m} / \mathrm{s}^{2}$$
Work Step by Step
From the graph, we pick two points on the curve: $(t, x)=(2.0 \mathrm{s}, 16 \mathrm{m})$ and $(3.0 \mathrm{s}, 27 \mathrm{m}) .$ The corresponding simultaneous equations are
$16 \mathrm{m}-0=v_{0}(2.0 \mathrm{s})+\frac{1}{2} a(2.0 \mathrm{s})^{2}$
$27 \mathrm{m}-0=v_{0}(3.0 \mathrm{s})+\frac{1}{2} a(3.0 \mathrm{s})^{2}$
Solving the equations lead to the values
$$v_{0}=6.0 \mathrm{m} / \mathrm{s}$$
$$and $$
$$a=2.0 \mathrm{m} / \mathrm{s}^{2}$$
