Question

If a single constant force acts on an object that moves on a straight line, the object's velocity is a linear function of time. The equation v = v_i + at gives its velocity v as a function of time, where a is its constant acceleration. What if velocity is instead a linear function of position? Assume that as a particular object moves through a resistive medium, its speed decreases as described by the equation v = v_i - kx, where k is a constant coefficient and x is the position of the object. Find the law describing the total force acting on this object.