The vertical acceleration of a certain solid-fuel rocket is given by a = ke^−bt − cv − g, where k, b, and c are constants, v is the vertical velocity acquired, and g is the gravitational acceleration, essentially constant for atmospheric flight. The exponential term represents the effect of a decaying thrust as fuel is burned, and the term −cv approximates the retardation due to atmospheric resistance. Determine the expression for the vertical velocity of the rocket t seconds after fi ring.