5. A store clerk moved a 4.4-kg box of soap without acceleration along a shelf by pushing it with a horizontal force of magnitude 8.1 N. If the employee did 5.9 J of work on the box, how far did the box move?

(a) assume the equation x = at^3 + bt describes the motion of a particular object, with x having the dimension of length and t having the dimension of time. determine the dimensions of the constants a and b. (use the following as necessary: l and t, where l is the unit of length and t is the unit of time.) (b) determine the dimensions of the derivative dx/dt = 3at^2 + b. (use the following as necessary: l and t, where l is the unit of length and t is the unit of time.)