The acceleration experienced by a moving boat after is engine is cut-off, is given by a = - k v 3 , where k is a constant. If v 0 is the magnitude of velocity at cut-off, then the magnitude of the velocity at time t after the cut off is

Step-by-step solution

Given, acceleration a = - k v 3 Initial velocity at cut-off, v 1 = v 0 Initial time of cut-off, t = 0 And final time after cut-off, t 2 = t Again, a = d v d t = - k v 3 Or d v v 3 = - k d t Integrating both sides, with in the condition of motion. ∫ v 0 v d v v 3 = - ∫ 0 t k d t Or - 1 2 v 2 v 0 v = - k t 0 t Or 1 2 v 2 - 1 2 v 0 2 = k t Or v = v 0 1 + 2 k t v 0 2