At any instant the velocity of a particle of mass $$500 \mathrm{~g}$$ is $$\left(2 t \hat{i}+3 t^{2} \hat{j}\right) \mathrm{ms}^{-1}$$. If the force acting on the particle at $$t=1 \mathrm{~s}$$ is $$(\hat{i}+x \hat{j}) \mathrm{N}$$. Then the value of $$x$$ will be:

As shown in the figure a block of mass 10 kg lying on a horizontal surface is pulled by a force F acting at an angle $$30^\circ$$, with horizontal. For $$\mu_s=0.25$$, the block will just start to move for the value of F : [Given $$g=10~\mathrm{ms}^{-2}$$]

Figures (a), (b), (c) and (d) show variation of force with time.

The impulse is highest in figure.

A block of mass $$5 \mathrm{~kg}$$ is placed at rest on a table of rough surface. Now, if a force of $$30 \mathrm{~N}$$ is applied in the direction parallel to surface of the table, the block slides through a distance of $$50 \mathrm{~m}$$ in an interval of time $$10 \mathrm{~s}$$. Coefficient of kinetic friction is (given, $$g=10 \mathrm{~ms}^{-2}$$):