The speed-time graph for a body moving along a straight line is shown in the figure. The average acceleration of the body may be .......... $m/s^2$.

The relation between time $t$ and distance $x$ is $t = \alpha x^2 + \beta x$,where $\alpha$ and $\beta$ are constants. The relation between acceleration $a$ and velocity $v$ is:

Statement $(I)$: An object subjected to velocities $\overrightarrow{v_1}$ and $\overrightarrow{v_2}$ has a resultant velocity with magnitude $|\vec{v}| = |\overrightarrow{v_1}| + |\overrightarrow{v_2}|$.
Statement $(II)$: The magnitude of displacement is either less than or equal to the path length of an object between two points.
Statement $(III)$: The instantaneous acceleration is the limiting value of the average acceleration as the time interval approaches zero.
Which of the following is correct?

An aircraft is flying at a height of $3400 \; m$ above the ground. If the angle subtended at a ground observation point by the aircraft positions $10.0 \; s$ apart is $30^{\circ}$,what is the speed in $m/s$ of the aircraft?

$A$ cyclist traversed half the distance of a linear track with a velocity $10 \ m \ s^{-1}$. The remaining part of the track was covered with a velocity $v_1$ for half the time and a velocity $v_2$ for the other half of the time. If $v_1+v_2=20 \ m \ s^{-1}$,then the average velocity of the cyclist during the completion of the journey through the track is (in $m \ s^{-1}$)

$A$ person of height $1.6 \ m$ is walking away from a lamp post of height $4 \ m$ along a straight path on the flat ground. The lamp post and the person are always perpendicular to the ground. If the speed of the person is $60 \ cm \ s^{-1}$,the speed of the tip of the person's shadow on the ground with respect to the person is . . . $cm \ s^{-1}$.