If \( A = \begin{pmatrix} 1 & 0 \\ 0 & -1 \end{pmatrix} \), \( P = \begin{pmatrix} 1 & 1 \\ 0 & 1 \end{pmatrix} \) and \( X = A P A^T \), then \( A^T X^{50} A = \)
A particle is moving in a straight line. The variation of position $ x $ as a function of time $ t $ is given as: $ x = t^3 - 6t^2 + 20t + 15 $. The velocity of the body when its acceleration becomes zero is: