A $2kg$ object slides along a rough floor (coefficient of sliding friction $= 0.3$)with initial velocity $(10 \mathrm{m}/\mathrm{s})\hat{\mathrm{i}}$. Find the motion of the object relative to car assuming that the coefficient of static friction is greater than $0.5$.

$a_1$ is due to pseudo force

$a_x=-(5+3)=-8 \mathrm{m}/{\mathrm{s}}^2$

Block will stop when

$$\begin{gathered} v_x=0=u_x+a_{x}t=10-8t \\ t=1.25 \mathrm{s} \end{gathered}$$

or at

So, for $t\le 1.25 \mathrm{s}$

$$\begin{gathered} x=x_0+u_{x}t+\frac{1}{2}{a}_x{t}^2 \\ =x_0+10t-4t^2 \\ {v}_x=u_x+a_{x}t=10-8t \end{gathered}$$

After this ${\mu }_{x}g>5 \mathrm{m}/{\mathrm{s}}^2$ as ${\mu }_3>0.5$

Therefore, now the block remains stationary with respect to car.