A particle slides down a frictionless parabolic $\left(y=x^2\right)$ track $\left(A-B-C\right)$ starting from rest at point $A$ as in figure. Point $B$ is at the vertex of parabola and point $C$ is at a height less than that of point $A$. After $C$, the particle moves freely in air as a projectile. If the particle reaches highest point at $P$, then

.

A cyclist starts from centre $O$ of a circular park of radius $1\mathrm{Km}$ and moves along the path OPRQO as shown in the figure. If he maintains the constant speed of $10{\mathrm{ms}}^{-1}$,what is his acceleration at point $R$ in magnitude and direction?

.

A particle is projected in the air at some angle to the horizontal, moves along the parabola as shown in the figure, where $x$ and $y$ indicate horizontal and vertical directions respectively. Show in the diagram, direction of velocity and acceleration at points $A,B$ and $C$.