An object moving with initial velocity u along a straight line attains maximum velocity v after travelling distance s. Assume the acceleration is uniform. Derive the relationship between position and velocity of the object by graphical method.

Please answer

We know that area under the velocity-time graph for a given interval of time represents the distance covered by a uniform accelerated object in a given time interval .
  From graph , acceleration, a = slope of velocity-time graph AB
  a = DB/AD  =DB/t  or DB = at
  Now distance travelled by object in time t is
  S = area of trapezium OABE
  = area of rectangle OADE + area of triangle ADB
  = OA*OE+1/2 DB*AD
 = ut+1/2 at2
 

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