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

The motion of an airplane is represented by a velocity-time graph as shown below. The distance covered by the airplane in the first $30.5 \ s$ is . . . . . . $km$.

Match Column-$I$ with Column-$II$ based on the distance-time $(d-t)$ graphs provided in the image.

$(1)$ Velocity decreases	$(a)$ Linear graph (constant slope)
$(2)$ Velocity increases	$(b)$ Concave up graph (increasing slope)
$(3)$ Velocity is constant	$(c)$ Concave down graph (decreasing slope)

The maximum possible acceleration of a train moving on a straight track is $10\ m/s^2$ and the maximum possible retardation is $5\ m/s^2$. If the maximum achievable speed of the train is $10\ m/s$,then the minimum time in which the train can complete a journey of $135\ m$ starting from rest and ending at rest is.........$s$.

$A$ particle starts from the origin at time $t = 0$ and moves along the positive $x-$ axis. The velocity-time graph is shown in the figure. What is the position of the particle at time $t = 5\,s$ (in $,m$)?

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