The loaded bucket of a craneachievers a maximum velocity 5 m//s in some time at a uniform rate and thentakes half of this time to stop at a uniform rate after the application of brake. The time differnce between the instants when half of the maximum velocity is achieved is t (sec). Find the displacement of the bucket.

The loaded bucket of a craneachievers a maximum velocity 5 m//s in som

1.	The loaded bucket of a craneachievers a maximum velocity 5 m//s in some time at a uniform rate and thentakes half of this time to stop at a uniform rate after the application of brake. The time differnce between the instants when half of the maximum velocity is achieved is t (sec). Find the displacement of the bucket.
Answer» Solution :VELOCITY time curve of the process is shown. Acceleration before applecation of brake, . `a_(1)=(v_(m))/(t_(1)) rArr t_(1)=v_(m)/(a_(1))` (i) DISPLACEMENT =`(1//2) v_(m)` `(t_(1)+t_(2)//2)` But velocity `(v_(m)//2)` is observed at `C` and `D`. `CD=Delta=Delta t=1 s` (given) `C` and `D` are mid-points of `OA` and `OB` . From similar TRIANGLES, `OB =(t_(1)_t_(2)//2) =2CD =2Delta t` Displacement=`((1)/(2)) v_(m) (2 Delta t)=v_(m) Delta t =5 xx1=5 m`,