A body is falling freely in a resistive medium. The motion of the body is described by \(\dfrac{dv}{dt}=(4-2v), \) where \(v\) is the velocity of the body at any instant (in \(\text{ms}^{–1}\)). The terminal velocity in this case refers to the velocity the body approaches as time \(t \to \infty.\) The initial acceleration and terminal velocity of the body, respectively, are:

The motion of a particle along a straight line is described by the equation \(x = 8+12t-t^3\) where \(x \) is in meter and \(t\) in seconds. The retardation of the particle, when its velocity becomes zero, is: