Question

A stationary 1.67 - kg object is struck by a stick. The object experiences a horiz ontal force given by F = at - bt 2 , where t is the time in milliseconds from the instant the stick first contacts the object. If a = 1500 N/(ms) and b = 20 N/(ms) 2 , what is the speed of the object just after it comes away from the stick at t = 2.74 ms

Answer 1

Newton's second law F= ma

given force equation is F = at - bt 2

                                   ma = at - bt 2    integrating on oth sides

                                  mv = a t^2/2 - b t^3/3

                                   v = 1/m(a t^2/2 - b t^3/3)

                                       = 1/1.76 (1500*(2.74*10^-3)^2 /2 - 20 (2.74*10^-3/3)^2

                                        = 3371.774 m/s