(Solved): The particle P moves upward along a parabolic surface defined by the equation y=4x2, where x and y ...

The particle $$P$$ moves upward along a parabolic surface defined by the equation $$y=4x^2$$, where $$x$$ and $$y$$ and in $$\mathrm{m}$$. When $$x=0.2\mathrm{m}$$, the particle speed is $$v=5\mathrm{m}/\mathrm{s}$$, and its speed is decreasing at a rate of $$8\mathrm{m}/{\mathrm{s}}^2$$. a. Determine the magnitude of the acceleration a of the particle $$P$$. b. On the figure below, draw the acceleration vector a at this instant (both components and resultant, as accurately as possible). Clearly label all vectors. c. On the figure below, draw the velocity vector $$\mathbf{v}$$ at this instant (as accurately as possible). d. Determine the horizontal and vertical components of the velocity vector $$\mathbf{v}$$ at this instant. Ans. $$a=30.83\mathrm{m}/{\mathrm{s}}^2;v_x=2.65\mathrm{m}/\mathrm{s};v_y=4.24\mathrm{m}/\mathrm{s}$$