Question

Block A and C starts from rest and moves to right with acceleration a(A)= 12t m/s² , a(C)=3m/s².Here t is in seconds.The time when block B again comes to rest is
(98 points question)

Answer 1

The block B will come to rest it means that the velocity of block B is zero.

The Blocks A,B,C are connected with the same rope.

By considering the portions of rope , we can see that the velocity of block B depends on Blocks A and C as...

velocity of block B (in downward)= (velocity of block A)/2 - (velocity of block C)/2

[By formula of constrained relation]

We are given accelerations. so velocity will be integration wrt time of acceleration.

so.......

Va = 6t^2 + c

Vc = 3t + c`

Here c and c` can be considered as initial velocity. these will be zero as blocks are at rest initially.

So.....

Vb= (Va - Vc)/2

Vb=(6t^2 - 3t)/2

Vb=0....

0 = (6t^2 -3t)/2

6t^2 -3t=0

t(6t-3)=0

t=0 or 6t-3=0

t=0 or t=1/2

Obviously Block is at rest at t=0 as given in question also ..XD

So at t=1/2sec block B will at rest

Answer 2

Answer:

Explanation:

Hope it helps you!....