$A$ bullet moving with a velocity of $200 \, cm/s$ penetrates a wooden block and comes to rest after traversing $4 \, cm$ inside it. What velocity is needed for travelling a distance of $9 \, cm$ in the same block? (in $cm/s$)

$A$ bullet fired into a target loses one-third of its velocity after travelling a distance $x$ meters into the target. If the bullet comes to rest by travelling a further distance $x^{\prime}$,then the ratio $\frac{x^{\prime}}{x}$ is

The initial velocity of a particle is $u$ at $t=0$ and the acceleration $a$ is given by $a = \alpha t^{3/2}$. Which of the following relations is valid?

If a body starts from rest and travels $120 \,cm$ in the $6^{th}$ second,what is the acceleration in $m/s^2$?

Two trains travelling on the same track are approaching each other with equal speeds of $40\ m/s$. The drivers of the trains begin to decelerate simultaneously when they are just $2.0\ km$ apart. Assuming the decelerations to be uniform and equal,the value of the deceleration to barely avoid collision should be..........$m/s^2$.

The velocity of a car travelling on a straight road is $3.6 \ km/h$ at an instant of time. Now,travelling with uniform acceleration for $10 \ s$,the velocity becomes exactly double. If the wheel radius of the car is $25 \ cm$,then which of the following is the closest to the number of revolutions that the wheel makes during this $10 \ s$?