Greatest displacement from a velocity function and the time intervals on which the acceleration is negative

A particle moves along a straight line and is at the fixed point \(O\) on the line when \(t=0\). Its velocity, \(v\text{ m s}^{-1}\), at time \(t\) seconds is given by \(v(t)=(2t^2-7t+3)e^{-0.4t}+3\sin t\), where \(0\leq t\leq6\).

1. Find the greatest displacement of the particle from \(O\).[4]
2. Determine the intervals of time during which the particle has negative acceleration.[3]