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

Two small blocks slide without losing contact with the surface along two frictionless tracks $1$ and $2$,starting at the same time with the same initial speed $v$. Track $1$ is perfectly horizontal,while track $2$ has a dip in the middle,as shown in the figure. Which block reaches the finish line first? [Hint: Use velocity-time graph to solve]

The velocity $v$ of a body moving along a straight line varies with time $t$ as $v = 2 t^2 e^{-t}$,where $v$ is in $m/s$ and $t$ is in $s$. The acceleration of the body is zero at $t =$

$A$ 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?

The position $x$ of a particle at any time $t$ is given by $x(t) = 4t^3 - 3t^2 + 2$. The acceleration and velocity of the particle at $t = 2 \, s$ are respectively:

The $x-t$ graph of a particle moving along a straight line is shown in the figure. The $v-t$ graph of the particle is correctly shown by: