2 The movement of a particle is described by the simple harmonic equation $$\ddot { x } = - 25 x$$ where \(x\) metres is the displacement of the particle at time \(t\) seconds, and \(\ddot { x } \mathrm {~m} \mathrm {~s} ^ { - 2 }\) is the acceleration of the particle. The maximum displacement of the particle is 9 metres. Find the maximum speed of the particle.
Circle your answer.
[0pt] [1 mark]
\(15 \mathrm {~m} \mathrm {~s} ^ { - 1 }\)
\(45 \mathrm {~m} \mathrm {~s} ^ { - 1 }\)
\(75 \mathrm {~m} \mathrm {~s} ^ { - 1 }\)
\(135 \mathrm {~m} \mathrm {~s} ^ { - 1 }\)