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Speed And Distance

The rate at which any moving body covers a particular distance is called its speed.
Distance = Speed × time
 
Unit : SI unit of speed is metre per second (mps). It is also measured in kilometers per hour (kmp) or miles per hour (mph).
 
Conversion of units :
  1. 1 hour = 60 minutes = 60 × 60 seconds.
     
    1 km = 1000 m
     
    1 km = 0.6214 mile
     
     1 mile = 1.609 km, i.e.,
     
    8 km = 5 miles
     
    1 yard = 3 feet
     
    1 foot = 12 inches
     
    1 km/h Description: 611.png m/sec,
     
    1 m/sec Description: 616.png km/h
     
    1 miles/hr Description: 621.pngft/sec
  2. Average speed Description: 626.png
  • If a certain distance (d), say from A to B, is covered at ‘a’ km/hr and the same distance is covered again say from B to A in ‘b’ km/hr, then the average speed during the whole journey is given by :
     
    Average speed = Description: 631.pngDescription: 636.png
  • If a body travels a distance ‘d’ from A to B with speed ‘a’ in time t1 and travels back from B to A i.e., the same distance with Description: 641.png of the usual speed ‘a’, then the change in time taken to cover the same distance is given by :
     
    Change in time = Description: 646.png × t1; for n > m Description: 652.png × t1; for m > n
  • If first part of the distance is covered at the rate of v1 in time t1 and the second part of the distance is covered at the rate of v2 in time t2, then the average speed is Description: 657.png
Relative Speed : When two bodies are moving in same direction with speeds S1 and S2 respectively, their relative speed is the difference of their speeds.
i.e.  Relative Speed = S1 – S2
When two bodies are moving in opposite direction with speeds S1 and S2 respectively, their relative speed is the sum of their speeds.
i.e.  Relative Speed = S1 + S2
  • If two persons (or vehicles or trains) start at the same time in opposite directions from two points A and B, and after crossing each other they take x and y hours respectively to complete the journey, then Description: 662.png 
  • A man covers a certain distance D. If he moves S1 speed faster, he would have taken t time less and if he moves S2 speed slower, he would have taken t time more. The original speed is given by Description: 667.png 
  • If a person with two different speeds U & V cover the same distance, then required distance
     
    Description: 672.png
     
    Also, required distance Description: 677.png  




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