The position vector of a particle is $\vec r = (a\cos \omega t)\hat i + (a\sin \omega t)\hat j$. The velocity of the particle is

A particle moves in east direction with $15 \,m/sec$. for $2\, sec$ then moves northward with $5\, m/sec$. for  $8 \,sec$. then average velocity of the particle is  

If the initial velocity in horizontal direction of a projectile is unit vector $\hat{i}$ and the equation of trajectory is $y =5 x (1- x )$. The $y$ component vector of the initial velocity is.

(Take $g=10\,m / s ^{2}$ )

A particle starts from rest and performing circular motion of constant radius with speed given by $v = \alpha \sqrt x$ where $\alpha$ is a constant and $x$ is the distance covered. The correct graph of magnitude of its tangential acceleration $(a_t)$ and centripetal acceleration $(a_c)$ versus $t$ will be:

A particle $(A)$ is dropped from a height and another particle $(B)$ is thrown in horizontal direction with speed of $5\; m/sec$ from the same height. The correct statement is