An object with mass m is dropped from rest and we assume that the air resistance is proportional to the speed of the object. if s(t) is the distance dropped after t seconds, then the speed is v = s'(t) and the acceleration is a = v'(t). i g is the acceleration due to gravity, then the downward force on the object is mg-cv, where c is positive constant, and newton's second law gives m = dv/dt = mg-cv (a) solve this as a linear equation to show that v=mg/c*(1-e^-ct/m) (b) what is the limiting velocity? (c) find the distance the object has fallen after t seconds.