Fill a flat tray with soft, damp sand and stand on the sand. How deep is the imprint that you make in the sand? Now put a block of wood on the sand and stand on the block and measure how far it sinks in. Explain your answer in both the cases.

(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.)