(Solved): A particle moves on the xy plane such that dtdx=t+11 for t0. At t=3, the tangent lin ...

A particle moves on the $\mathrm{x}-\mathrm{y}$ plane such that $\frac{dx}{dt}=\frac{1}{\sqrt{t+1}}$ for $t\ge 0$. At $\mathrm{t}=3$, the tangent line to the curve traced by the particle is given by $y=4x+2$. (a) Find the velocity vector and the speed of the particle at $t=3$. (b) Suppose that at $\mathrm{t}=0$, the $\mathrm{x}$-coordinate of the particle is 6 . Find the position of the particle at $\mathrm{t}=3$. (c) Is the particle ever at rest? Justify your answer.