Solve the following :
Question:

Suppose the block of the previous problem is pushed down the incline with a fame of $4 \mathrm{~N}$. How far will the block move in the first two seconds after starting from rest? The mass of the block is $4 \mathrm{~kg}$.

Solution:

Along inclined plane

$F_{N}=m a$

$F+m g \sin 30-f f_{k}=m a$

$4+4(10)\left(\frac{1}{2}\right)-\mu_{k} m g \cos 30^{\circ}=m a$

$24-0.11 \times 4 \times 10 \times \frac{\sqrt{3}}{2}=4 a$

$a=5 \mathrm{~m} / \mathrm{s}^{2}$

Now,

$u=0 \frac{m}{s} ; t=2 s ; a=5 \mathrm{~m} / \mathrm{s}^{2}$

$s=u t+\frac{1}{2} a t^{2}$

$s=0+\frac{1}{2}(5)(2)^{2}$

$\mathrm{s}=10 \mathrm{~m}$