A vehicle moves along a straight road. The vehicle's position is given by f(t) , where tt is measured in seconds since the vehicle starts moving. During the first 10 seconds of the motion, the vehicle's acceleration is proportional to the cube root of the time since the start. Which of the following differential equations describes this relationship, where k is a positive constant?

a. df/dt = kſ
b. df/dt - = kgf
c. d²f/dt = kyt dt2
d. d²f/dt = ky