A particle moves in $x-y$ plane with velocity $\vec v = a\widehat i\, + \,bx\widehat j$ where $a$ & $b$ are constants. Initially particle was at origin then trajectory equation is:-

- A
$y = \frac{a}{b}x - \frac{1}{2}b{x^2}$

- B
$y = x - \frac{{b{x^2}}}{{2a}}$

- C
$y = \frac{{b{x^2}}}{{2a}}$

- D
None of above

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

Find the value of Relative velocity of any two particles moving in a frame of reference.

A particle moves in a plane along an elliptic path given by $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$. At point $(0, b)$, the $x$-component of velocity is $u$. The $y$-component of acceleration at this point is

- [KVPY 2011]

A person walks $25.0^{\circ}$ north of east for $3.18 \,km$. How far would she have to walk due north and then due east to arrive at the same location?

- [KVPY 2016]

Which is the direction of instantaneous velocity for angular path ?