The velocity of a particle moving along the $x$-axis varies as a function of time $t$ as $v(t) = (1 - 3t^2 + 2t^3) \ m/s$. If its position at $t = 0$ is $x = 0$, then at $t = 2 \ s$, its position is: (in $m$)

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 $10 \ s$?

If a body loses half of its velocity on penetrating $3 \, cm$ in a wooden block,then how much will it penetrate more before coming to rest? (in $cm$)

The velocity of a particle is $v = v_{0} + gt + Ft^{2}$. Its position is $x = 0$ at $t = 0$; then its displacement after time $t = 1$ is:

The initial velocity of a particle moving along the $x$-axis is $u$ (at $t=0$ and $x=0$) and its acceleration $a$ is given by $a=kx$. Which of the following equations is correct for its velocity $(v)$ and position $(x)$?

The displacement of a particle starting from rest at $t=0$ is given by $s=9 t^2-2 t^3$. The time in seconds at which the particle will attain zero velocity is (in $s$)