A small spherical body is dropped from rest into a deep tank of viscous fluid. The fluid exerts a viscous drag force on the body that is directly proportional to its velocity. Which of the following statements correctly describes the graph of the body's acceleration a versus its velocity v ?

Step-by-step solution

The equation of motion for a body falling in a viscous fluid is given by ma = mg_ eff - kv , where g_ eff is the effective acceleration due to gravity (accounting for buoyancy) and kv is the viscous drag force. Rearranging this equation for acceleration a , we get: a = g_ eff - ( k m )v This equation is of the form y = c - mx , which represents a straight line with a negative slope ( -k/m ) and a positive y-intercept ( g_ eff ). When v = 0 , a = g_ eff (positive acceleration axis intercept). When a = 0 , v = mg_ ef