  In the history of first-order algorithms, Nesterov's accelerated gradient
descent (NAG) is one of the milestones. However, the cause of the acceleration
has been a mystery for a long time. It has not been revealed with the existence
of gradient correction until the high-resolution differential equation
framework proposed in [Shi et al., 2021]. In this paper, we continue to
investigate the acceleration phenomenon. First, we provide a significantly
simplified proof based on precise observation and a tighter inequality for
$L$-smooth functions. Then, a new implicit-velocity high-resolution
differential equation framework, as well as the corresponding implicit-velocity
version of phase-space representation and Lyapunov function, is proposed to
investigate the convergence behavior of the iterative sequence
$\{x_k\}_{k=0}^{\infty}$ of NAG. Furthermore, from two kinds of phase-space
representations, we find that the role played by gradient correction is
equivalent to that by velocity included implicitly in the gradient, where the
only difference comes from the iterative sequence $\{y_{k}\}_{k=0}^{\infty}$
replaced by $\{x_k\}_{k=0}^{\infty}$. Finally, for the open question of whether
the gradient norm minimization of NAG has a faster rate $o(1/k^3)$, we figure
out a positive answer with its proof. Meanwhile, a faster rate of objective
value minimization $o(1/k^2)$ is shown for the case $r > 2$.
