A particle starts moving from rest in a straight line with constant acceleration. After time $t_0$, acceleration changes its sign (just opposite to the initial direction), remaining the same in magnitude. Determine the time from the beginning of motion in which the particle returns to the initial position.
$2 t_0$
$(2+\sqrt{2}) t_0$
$3 t_0$
$(2-\sqrt{2}) t_0$
An automobile, travelling at $40\, km/h$, can be stopped at a distance of $40\, m$ by applying brakes. If the same automobile is travelling at $80\, km/h$, the minimum stopping distance, in metres, is (assume no skidding)..........$m$
A rocket is moving in a gravity free space with a constant acceleration of $2 \ ms ^{-2}$ along $+x$ direction (see figure). The length of a chamber inside the rocket is $4 \ m$. A ball is thrown from the left end of the chamber in $+x$ direction with a speed of $0.3 \ ms ^{-1}$ relative to the rocket. At the same time, another ball is thrown in $-x$ direction with a speed of $0.2 \ ms ^{-1}$ from its right end relative to the rocket. The time in seconds when the two balls hit each other is:
A particle starting from rest and moving with a uniform acceleration along a straight line covers distances $a$ and $b$ in successive intervals of $p$ and $q$ second. The acceleration of the particle is