Question: The motion of a set of particles moving along the x-axis is governed by the differential equation

where \(x\left( t \right)\) denotes the position at time t of the particle

(a) If a particle resides at x = 1 when t = 2, what is the velocity of the particle?

(b) Derive the acceleration of the particle denoted by \(\frac{{{d}^{2}}x}{d{{t}^{2}}}\) as a function of x and t.