Question

The vertical displacement of block A in
meter is given by y = t^2/4 where t is in
second. Calculate the downward
acceleration as of block B.​

Answer 1

Answer:

on doble differentiating we get 1/2.

now using constraint relationship we get -GB+8ga=0

GB=8×1/2=4m/s²

Answer 2

The downward acceleration as of block B is 4 m/s²

Given,

The vertical displacement of block A, $y= \frac{t^{2} }{4}$

and t is second.

To Find,

Find the downward acceleration as of block B.

Solution,

• What is downward acceleration:- A downward acceleration could indicate either the object is travelling upward (has an upward velocity) and slowing down, or the object is travelling downward (has a downward velocity) and speeding up. The acceleration is still downward even at the trajectory's highest point. The projectile simply experiences a shift in direction from upward to downward at the peak, when the vertical velocity is zero.

According to the question, the vertical displacement of block A = $S_{A}$

and,$S_{A} = y$

2y length of thread is unfolded which will move B 2y distance.

similarly for 3 navable disc

$y_{B} = 2*2*2*y= 8y$

$y= \frac{t^{2} }{4}$

$\frac{dy}{dt} = \frac{2t}{4} =\frac{t}{2}$

$\frac{d^{2}y }{dt^{2} } = \frac{1}{2}$

$y_{B} = \frac{d^{2} y}{dt^{2} } \\= > y_{B} = 8*\frac{d^{2} y}{dt^{2} }\\= > y_{B} = 8*\frac{1}{2} \\= > y_{B} =4$

Hence, the downward acceleration as of block B is 4 m/s²

#SPJ3