The work done by a force $\vec F = \left( { - 6{x^3}\hat i} \right)\,N$ in displacing a particle from $x = 4\,m$ to $x = -2\,m$ is ............... $\mathrm{J}$

A car is moving on a straight horizontal road with a speed $v.$ If the coefficient of friction between the tyres and the road is $\mu ,$ the shortest distance in which the car can be stopped is

The mass of the bob of a simple pendulum of length $L$ is $m$. If the bob is left from its horizontal position then the speed of the bob and the tension in the thread in the lowest position of the bob will be respectively

A force acts on a $3\, gm$ particle in such a way that the position of the particle as a function of time is given by $x = 3t -4t^2 + t^3$, where $x$ is in $meters$ and $t$ is in $seconds$ . The work done during the first $4\, second$ is .............. $\mathrm{mJ}$

In an elastic collision of two particles the following quantity is conserved

A mass $m$ moving horizontally with velocity $v_0$ strikes a pendulum of mass $m$. If the two masses stick together after the collision, then the maximum height reached by the pendulum is