An alpha particle enters a hollow tube of $4 \, m$ length with an initial speed of $1 \, km/s$. It is accelerated in the tube and comes out of it with a speed of $9 \, km/s$. The time for which it remains inside the tube is

$A$ particle initially at rest starts moving from reference point $x=0$ along the $x$-axis,with velocity $v$ that varies as $v=4 \sqrt{x} \ m/s$. The acceleration of the particle is . . . . . . $m/s^2$.

$A$ particle experiences a constant acceleration for $20 \,s$ after starting from rest. If it travels a distance ${S_1}$ in the first $10 \,s$ and a distance ${S_2}$ in the next $10 \,s$,then:

$A$ car moving at a speed of $50 \, km/hr$ stops after covering a distance of $6 \, m$ upon applying brakes. If the same car is moving at a speed of $100 \, km/hr$,what distance (in $m$) will it cover after applying the brakes?

Tripling the speed of the motor car multiplies the distance needed for stopping it by

Two particles $A$ and $B$ start from rest and move for equal time on a straight line. Particle $A$ has an acceleration of $2\,m/s^2$ for the first half of the total time and $4\,m/s^2$ for the second half. The particle $B$ has acceleration $4\,m/s^2$ for the first half and $2\,m/s^2$ for the second half. Which particle has covered a larger distance?