A particle \(P\) moves in a straight line with simple harmonic motion. The period of the motion is \(\frac { \pi } { 4 }\) seconds. At time \(t = 0 , P\) is at rest at the point \(A\) and the acceleration of \(P\) has magnitude \(20 \mathrm {~m} \mathrm {~s} ^ { - 2 }\).
Find
the amplitude of the motion,
the greatest speed of \(P\) during the motion,
the time \(P\) takes to travel a total distance of 1.5 m after it has first left \(A\).