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the only force acting on a 2.0 kg body as it moves along the x axis has an x component f = -6x where x is in meters. the velocity of body at x = 3m is 8m/s. what is the velocity at x=4m at what position value of x will have v = 5m/s

the only force acting on a 2.0 kg body as it moves along the x axis has an x component f = -6x where x is in meters. the velocity of body at x = 3m is 8m/s. 
  1. what is the velocity at x=4m
  2. at what position value of x will have v = 5m/s

Grade:11

1 Answers

Pavan Kumar
32 Points
5 years ago
hey, thank you for asking the question man,
 
the first thing you need to know    f=m*v*dv/dx
                        force=mass*velocity*derivative of velocity w.r.t displacement
                        proof:   f=m*a     [a=accleration]
                                     a=dv/dt   *  [ dx/dx]
                                     a=dv/dx  *  dx/dt
                                       = dv/dx * v
                                    f=m*dv/dx * v
so   given f=-6x  
                           f= 2 * v* dv/dx = -6x
                                 v dv = -3xdx
                                  v2/2 = -3x2/2 + constant 
                             given at x=3 , v= 8 substituting in the above equation we get  c= 91/2
                                     so just substitute the given readings that they have asked 
have a good day.
                                     

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