The co-ordinates of a particle moving in $$x$$-$$y$$ plane are given by : $$x=2+4 \mathrm{t}, y=3 \mathrm{t}+8 \mathrm{t}^2$$.

The motion of the particle is :

Train A is moving along two parallel rail tracks towards north with speed $$72 \mathrm{~km} / \mathrm{h}$$ and train B is moving towards south with speed $$108 \mathrm{~km} / \mathrm{h}$$. Velocity of train B with respect to A and velocity of ground with respect to B are (in $$\mathrm{ms}^{-1}$$):

The relation between time '$$t$$' and distance '$$x$$' is $$t=\alpha x^2+\beta x$$, where $$\alpha$$ and $$\beta$$ are constants. The relation between acceleration $$(a)$$ and velocity $$(v)$$ is :

Projectiles A and B are thrown at angles of $$45^{\circ}$$ and $$60^{\circ}$$ with vertical respectively from top of a $$400 \mathrm{~m}$$ high tower. If their ranges and times of flight are same, the ratio of their speeds of projection $$v_A: v_B$$ is :

[Take $$g=10 \mathrm{~ms}^{-2}$$]