Math Formulae: Time, Speed, and Distance

 

1. Distance = Speed × Time
   
   
2. Speed = 

   	Distance
   	Time

   
   
   
3. Time = 

   	Distance
   	Speed

   
   
   
4. 1 km/hr = 

   	5
   	18

    m/s       
   1 m/s = 

   	18
   	5

    km/h
   
   
5. Average Speed = 

   	Total Distance
   	Total Time

   
   
   
6. When half distance is covered with speed of x km/h and other half with y km/h, then
         Average Speed = 

   	2xy
   	x + y

   
   
   
7. When equal distances are covered with speed of x km/h, y km/h, and z km/h, then
         Average Speed = 

   	3xyz
   	xy + yz + zx

   
   
   
8. When two bodies are moving in same direction with speed of x km/h and y km/h, then their
         Relative Speed = (x - y) km/h,     if x > y       Relative Speed = (y - x) km/h,     if x < y
   
   
9. When two bodies are moving in opposite direction with speed of x km/h and y km/h, then their
         Relative Speed = (x + y) km/h
   
   

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10. Boats and Streams:
    If A is speed of current,
    B is speed of Boat,
    U is downstream speed of boat, and
    V is upstream speed of boat, then
    
    
    • U = B + A
      
      
    • V = B - A,     B > A
      
      
    • Speed of boat in still water = 

      	U + V
      	2

      
      
      
    • Speed of current = 

      	U - V
      	2

      
      
      

    • 	Time taken by Boat in Downstream
      	Time taken by Boat in Upstream

        =   

      	Upstream Speed
      	Downstream Speed

      
      
      
    
    
    

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11. Circular Motion:
    • When two bodies start moving along a circular path at same time, then time taken by the bodies to meet first time = 

      	Length of circular path
      	Relative Speed

      
      
      
    • When two bodies start moving along a circular path at same time, and take t₁ and t₂ time to complete one round then time taken to meet at starting point  =  LCM of t₁ and t₂.
    
    
    

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