The speed of an engine is proportional to the square root of the number of wagons attached to it.Without any wagons attached to it the speed of the engine is 60 km/hr.With 16 wagons attached to it the speed of the engine is 40 km/hr.Find the maximum number of wagons that can be attached so that the train moves.

• Let v be speed and n be the number of wagons attached.
  
  v = c1*(n^0.5)+c2 be the equation where c1 and c2 are constants
  
  when n=0, v=c2 => c2=60
  
  when n=16, 40=4*c1 + 60 => c1=-5
  
  Therefore the eqn is v = 60 - 5(n^0.5)
  
  When v=0, n=144. Hence 143 is the maximum number of wagons that can be attached so that the train moves.
• 12 years agoHelpfull: Yes(6) No(5)
• we have the original speed as 60km/hr
  
  now speed is directly proportional to square root of no. of wagon;
  
  hence speed = k *sqrt(no. of wagons) (where k is proportionality constant)
  
  hence ; reduced speed 40 = 60 - k*sqrt(no. of wagons)
  
  i.e; 40 = 60 - k*4
  hence, k= 5.
  
  hence for engine to stop,speed =0
  0 = 60 - 5*sqrt(n)
  
  =>sqrt(n)=12
  =>n =144
  if our engine should continue to move, we need 144-1 =143 wagons.
  
• 8 years agoHelpfull: Yes(1) No(1)