$A$ particle moves for $8 \, s$. It first accelerates from rest and then retards to rest. If the retardation is $3 \, times$ the acceleration, then the time for which it accelerates is: (in $s$)

$A$ particle moves in a straight line with a constant acceleration. It changes its velocity from $10 \, m/s$ to $20 \, m/s$ while passing through a distance of $135 \, m$ in $t$ seconds. The value of $t$ is..........$s$.

$A$ body $A$ starts from rest with an acceleration $a_1$. After $2$ seconds,another body $B$ starts from rest with an acceleration $a_2$. If they travel equal distances in the $5$th second after the start of $A$,then the ratio $a_1:a_2$ is equal to

$A$ 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:

$A$ bullet enters a wooden block with velocity $120 \,m/s$. The bullet travels $1.5 \,s$ in the block before its velocity reduces to zero due to a resistance force which is proportional to the square root of the velocity. The distance travelled by the bullet in the wooden block is (in $\,m$)

$A$ particle starts from origin $O$ from rest and moves with a uniform acceleration along the positive $x$-axis. Identify all figures that correctly represent the motion qualitatively. ($a =$ acceleration,$v =$ velocity,$x =$ displacement,$t =$ time)