Position Function From Acceleration
A particle moves along the $$x$$-axis such that for any time $$t \geq 0$$, its acceleration is given by $$a(t) = 4t^3 - 6t$$. If the velocity of the particle at time $$t=0$$ is $$v(0) = 1$$ and its position at time $$t=0$$ is $$x(0) = -1$$, then the position of the particle at time $$t$$ is $$x(t) =$$
A
$$\frac{1}{5}t^5 - t^3 + t - 1$$
B
$$\frac{4}{5}t^5 - 3t^3 + t - 1$$
C
$$\frac{1}{5}t^5 - t^3 + t + 1$$
D
$$t^4 - 3t^2 + t - 1$$
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