C

Step 1: Consider the motion of a lead shot falling through glycerine. The drag force acting on the shot increases with velocity, leading to terminal velocity as it falls through the fluid.
Step 2: At the beginning, the velocity increases rapidly, but as the drag force becomes significant, this increase slows down. Eventually, the shot reaches a constant terminal velocity where the forces (weight and drag) balance.
Step 3: The velocity versus distance graph will initially show a concave upward curve (characteristic of increasing velocity) and then gradually flatten out as it approaches terminal velocity, which fits the graph depicted in Option C.
Therefore, the correct answer is C.