What would be the stopping distance if the velocity of a vehicle becomes three times (in $d$)?

An open knife edge of mass $50 \ g$ is dropped from a height $2 \ m$ on a wooden floor. If the blade penetrates up to a depth of $10 \ cm$ into the wood,the average resistance offered by the wood to the knife edge is $....N$

$A$ pendulum bob on a $2\, m$ string is displaced $60^\circ$ from the vertical and then released. What is the speed of the bob as it passes through the lowest point in its path? (Take $g = 9.8\, m/s^2$)

$A$ ball of mass $1 \ kg$ moves in a straight line with velocity $v = c x^\alpha$, where $c = 1$ ($SI$ unit) and $\alpha$ is a constant. If the work done by the net force during its displacement from $x = 0$ to $x = 4 \ m$ is $128 \ J$, then the value of $\alpha$ is

The velocity-time graph for a body of mass $10\, kg$ is shown in the figure. The work done on the body in the first two seconds of the motion is ................ $J$.

$A$ body is projected vertically upwards with a velocity of $20 \,m \,s^{-1}$. If the potential energy of the body at a height of $5 \,m$ from the ground is $100 \,J$, then the kinetic energy of the body at a height of $10 \,m$ from the ground is (Acceleration due to gravity $= 10 \,m \,s^{-2}$) (in $\,J$)