The following data is given for the velocity of a body as a function of time. It is required to find the velocity at t = 21 sec. For this purpose, a quadratic polynomial v(t) = at2 + bt + c is to be used.The velocity profile is given ast in sec 0 13141518202224V in m/sec 0225248.5316.6517.35535.35570589.5The correct set of equations that will find a, b and c is

• A. \(\begin{bmatrix} 169 &13 &1 \\ 225&15 &1 \\ 324&18 &1 \end{bmatrix}\begin{bmatrix} a\\ b\\ c \end{bmatrix} = \begin{bmatrix} 248.5\\ 316.6\\ 517.35 \end{bmatrix}\)
• B. \(\begin{bmatrix} 176 &14 &1 \\ 225&15 &1 \\ 400&20 &1 \end{bmatrix}\begin{bmatrix} a\\ b\\ c \end{bmatrix} = \begin{bmatrix} 248.5\\ 316.6\\ 535.35 \end{bmatrix}\)
• C. \(\begin{bmatrix} 169 &13 &1 \\ 196&14 &1 \\ 225&15 &1 \end{bmatrix}\begin{bmatrix} a\\ b\\ c \end{bmatrix} = \begin{bmatrix} 225\\ 248.5\\ 316.6 \end{bmatrix}\)
• D. \(\begin{bmatrix} 324 &18 &1 \\ 484&22 &1 \\ 225&15 &1 \end{bmatrix}\begin{bmatrix} a\\ b\\ c \end{bmatrix} = \begin{bmatrix} 517.35\\ 589.5\\ 316.6 \end{bmatrix}\)