Question

Blocks $A$ and $C$ start from rest and move to the right with accelerations $a_A=12t{\text{m/s}}^2$ and $a_C=3{\text{m/s}}^2$ respectively. Here $t$ is in seconds. The time when block $B$ again comes to rest is (Given that sytem starts from rest and surface is smooth).

• A. $2\text{s}$
• B. $1\text{s}$
• C. $\frac{3}{2}\text{s}$
• D. $\frac{1}{2}\text{s}$

Answer 1

The correct option is D $\frac{1}{2}\text{s}$

B will come to rest when velocity of block A and C becomes equal i.e.
$V_A=V_C$
Finding $V_A$ and $V_C$
Acceleration of block A, $a_A=\frac{d{V}_A}{dt}=12t$
$\Rightarrow {\int }_0^{V_A}dv={\int }_0^{t}12t.dt$
$\Rightarrow V_A=\frac{12t^2}{2}\Rightarrow V_A=6t^2$
and
$V_C=u_C+a_{C}t=0+3\left(t\right)=3t$
When $V_A=V_C$
$\Rightarrow 6t^2=3t$
$\Rightarrow t=\frac{1}{2}$ seconds