A particle projected from origin moves in $x-y$ plane with a velocity $\vec{v}=3 \hat{i}+6 x \hat{j}$, where $\hat{i}$ and $\hat{j}$ are the unit vectors along $x$ and $y$ axis. Find the equation of path followed by the particle

The height $y$ and the distance $x$ along the horizontal plane of a projectile on a certain planet (with no surrounding atmosphere) are given by $y = (8t - 5{t^2})$ meter and $x = 6t\, meter$, where $t$ is in second., the acceleration due to gravity is given by ......... $m/{\sec ^2}$

A particle is moving with velocity $\vec v = K(y\hat i + x\hat j)$ where $K$ is a constant. The general equation for its path is

Velocity of a particle moving in a curvilinear path in a horizontal $X$ $Y$ plane varies with time as $\vec v = (2t\hat i + t^2 \hat j) \ \  m/s.$ Here, $t$ is in second. At $t = 1\  s$

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