Suppose the acceleration of an object moving along a line is given by a(t) = -kv(t), where k is a positive constant and v is the object’s velocity. Assume that the initial velocity and position are given by v(0) = 10 and s(0) = 0, respectively.

a. Use a(t) = v'(t) to find the velocity of the object as a function of time.

b. Use v(t) = s'(t) to find the position of the object as a function of time.

c. Use the fact that dv/dt = (dv/ds)(ds/dt) (by the Chain Rule) to find the velocity as a function of position.