To find X0, V0, and a, we will first differentiate the given equation with respect to t:

X = 2 + 2t + t^2
V = dX/dt = 2 + 2t

From the above equation, we can see that V0 = V(0) = 2

Now, differentiating V with respect to t, we get:

a = dV/dt = d/dt(2 + 2t) = 2

Therefore, X0 = X(0) = 2, V0 = 2, a = 2

To find V(t), we can directly plug in the value of t into the equation for V:

V(t) = 2 + 2t

To find S(t), we need to integrate V(t) with respect to t:

S(t) = ∫V(t) dt
S(t) = ∫(2 + 2t) dt
S(t) = 2t + t^2 + C

Given that V(5) is being asked, we can calculate V(5) as follows:

V(5) = 2 + 2(5) = 12

Therefore, V(5) = 12