Match Column-$I$ with Column-$II$:

The displacement-time graphs of two moving particles make angles of $30^{\circ}$ and $45^{\circ}$ with the time axis. The ratio of their velocities is

$y = (P t^2 - Q t^3) \ m$ is the vertical displacement of a ball which is moving in a vertical plane. Then the maximum height that the ball can reach is,

For the following velocity-time graph, the average speed for the motion during first $80 \, s$ is

$A$ particle covers a distance from $A$ to $B$ over a period of time; the distance versus time plot is shown below. Then which of the following is true for the motion of the particle?

$A$ particle is moving along the $Y$-axis. The position of the particle from the origin as a function of time $(t)$ is given as $y(t) = 10 t e^{-2 t}$. How far is the particle from the origin when it stops momentarily? ($y$ is given in units of metre and $t$ is in units of second)