2-1. The initial velocity of the block is , and the initial position of the block is . If a normally distributed force  is applied to the rope and the coefficient of kinetic friction between the 100-kg block and the ground is . Determine the means and standard deviations of the position and velocity of the block when .

Solution

Referring to the free-body diagram of the block, we have

                                                                      

 

 

 

 

 

Therefore

 

                                   

   

                                                                                              

                         

  

 

                                       

 

Therefore,  and .                                        Ans.