A rocket moves straight upward with zero initial velocity and with an acceleration $20 \mathrm{~m} / \mathrm{s}^2$. It runs out of fuel and stops accelerating at the end of 5th second. It reaches a maximum height and falls back to the earth. The speed when it hits the ground is (take $g=10 \mathrm{~m} / \mathrm{s}^2$ )

A particle moves along a straight line, such that its displacement $x$ varies with time $t$ as $x=\alpha t^3+\beta t^2+\gamma$, where $\alpha, \beta$ and $\gamma$ are constants, $v_1$ is the average velocity of the particle during its journey between $t=1 \mathrm{~s}$ and $t=3 \mathrm{~s} . v_2$ is the instantaneous velocity of the particle at $t=3 \mathrm{~s}$. The ratio $\frac{v_1}{v_2}$ is

An aircraft is flying at a height of $h$ above the ground and at a speed of $v$. The maximum angle subtended at a ground observation point by the aircraft after time $t$ is

A particle starts from rest. Its acceleration (a) versus time $(t)$ graph is as shown in the figure. The maximum speed of the particle will be