Question 1028019
Given a(t), we can integrate to find v(t)...
{{{v(t) = integral(a(t) dt) = integral(6t - 2) dt = 3t^2 - 2t + C[1]}}}
Now when t = 0, v = 2, so we can find the first constant...
{{{C[1] = 2}}} so that
{{{v(t) = 3t^2 - 2t + 2}}}
Now integrate once again to find position...
{{{x(t) = integral(3t^2 - 2t + 2) dt = t^3 - t^2 + 2t + C[2]}}}
Now when t = 0, x = 2, we have
{{{C[2] = 2}}}
and
{{{x(t) = t^3 - t^2 + 2t + 2}}}