Question

20. The loaded bucket of a crane achieves a maximum velocity
5 m/s in some time at a uniform rate and then takes half of
this time to stop at a uniform rate after the application of
brake. The time difference between the instants when half
of the maximum velocity is achieved is t (sec). Find the
displacement of the bucket.
of the​

Answer 1

Answer :

5m

Solution :

Velocity time curve of the process is shown. Acceleration before applecation of brake,

.

a1=vmt1⇒t1=vma1 (i)

Displacement =(1/2)vm

(t1+t2/2)

But velocity (vm/2) is observed at C and D.

CD=Δ=Δt=1s (given)

C and D are mid-points of OA and OB .

From similar triangles, OB=(t1_t2/2)=2CD=2Δt

Displacement=(12)vm(2Δt)=vmΔt=5×1=5m,