An object of mass m kg is projected vertically upward from the ground with initial velocity u ms^(-1). Assume that the forces acting on the object are the gravitational fiorce and the retarding force due to air resistance with a magnitude of α |v|, where α is a positive constant and v is the velocity of the object at time t.

Show that the motion of the object can be modelled by the differential equation:

m(dv/dt) = -αv-mg, where g is the acceleration due to gravity.

Question

An object of mass m kg is projected vertically upward from the ground with initial velocity u ms^(-1). Assume that the forces acting on the object are the gravitational fiorce and the retarding force due to air resistance with a magnitude of α |v|, where α is a positive constant and v is the velocity of the object at time t.

Show that the motion of the object can be modelled by the differential equation:

m(dv/dt) = -αv-mg, where g is the acceleration due to gravity.