Question

Block $C$ shown in figure, starts from rest and moves downward with a constant acceleration. Knowing that after $1.2s$ the velocity of block $A$ is $7.2\frac{m}{s},$ the displacement (in metres) of block $C$ after $8s$ is

Answer 1

Since work done by tension in an ideal thread/ rope is always zero.
$\Rightarrow W_{net}^{T_2}=0\Rightarrow -2T_{2}y+3T_{2}z=0$
$\Rightarrow 2y=3z$
Differentiating twice
$2a_A=3a_B$
$\Rightarrow a_B=\frac{2a_A}{3}$

$W_{net}^{T_1}=0\Rightarrow -2T_{1}x+T_{1}z=0$
$\Rightarrow 2x=z$
Differentiating twice
$\Rightarrow 2a_c=a_B$
$\Rightarrow a_c=\frac{a_B}{2}$

Since $A$ starts from rest, $B$ and $C$ also start from rest.

For $A$
$v_A=u_A+a_{A}t$
$7.2=0+a_A\left(1.2\right)$
$\Rightarrow a_A=6m{s}^{-2}$
$\Rightarrow a_B=\frac{2}{3}\left(6\right)=4m{s}^{-2}$
$\Rightarrow a_c=\frac{4}{2}=2m{s}^{-2}$
Using equation of motion, displacement of block $C$ is
$S_c=u_{c}t+\frac{1}{2}\left(a_c\right)(8{)}^2$
$S_c=0+\frac{1}{2}\left(2\right)(8{)}^2=64m$