Air is delivered through a constant-diameter duct by a fan. The air is inviscid, so the fluid velocity profile is "flat" across each cross section. During the fan start-up, the following velocities were measured at the time \(t\) and axial positions \(x\) :

\[ \begin{array}{llll} & \boldsymbol{x}=\mathbf{0} & \boldsymbol{x}=\mathbf{1 0} \mathbf{~ m} & \boldsymbol{x}=\mathbf{2 0} \mathbf{~ m} \\ t=0 \mathrm{~s} & V=0 \mathrm{~m} / \mathrm{s} & V=0 \mathrm{~m} / \mathrm{s} & V=0 \mathrm{~m} / \mathrm{s} \\ t=1.0 \mathrm{~s} & V=1.00 \mathrm{~m} / \mathrm{s} & V=1.20 \mathrm{~m} / \mathrm{s} & V=1.40 \mathrm{~m} / \mathrm{s} \\ t=2.0 \mathrm{~s} & V=1.70 \mathrm{~m} / \mathrm{s} & V=1.80 \mathrm{~m} / \mathrm{s} & V=1.90 \mathrm{~m} / \mathrm{s} \\ t=3.0 \mathrm{~s} & V=2.10 \mathrm{~m} / \mathrm{s} & V=2.15 \mathrm{~m} / \mathrm{s} & V=2.20 \mathrm{~m} / \mathrm{s} \end{array} \]

Estimate the local acceleration, the convective acceleration, and the total acceleration at \(t=1.0 \mathrm{~s}\) and \(x=10 \mathrm{~m}\). What is the local acceleration after the fan has reached a steady air flow rate?