a) A block of mass m = 0.53 kg slides on a horizontal surface with an initial speed v0 = 1.47 m/s. The coefficient of kinetic friction between the block and the surface is muk = 0.130. In addition to the kinetic frictional force, a drag force also acts on the block and is given by F=kmv^2, where k = 4.09 1/m. How much time does it take for the block to come to rest? (Note: Generate a symbolic answer and learn how to this integral by hand...)
b) How far will the block have moved by the time it comes to rest? (Note: Generate a symbolic answer and learn how to do this integral by hand...)
c) If the initial speed of the block is increased to infinity, it turns out that the time taken for the block to come to a rest approaches a finite value whereas the distance traveled approaches infinity. Suppose the initial speed of the block is increased. Find the maximum time taken for the block to come to a rest. Is this a paradox?