Work Energy and...

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:

The work done by the frictional force on a surface in drawing a circle of radius r on the surface by a pencil of negligible mass with a normal pressing force N (coefficient of friction $$\mu_k$$ ) is : 

A bead is free to slide down a smooth wire tightly stretched between points $$A$$ and $$B$$ on a verticle circle of radius $$R$$. If the bead starts from rest at '$$A$$', the highest point on the circle, its velocity when it arrives at $$B$$ is

A bob hangs from a rigid support by an inextensible string of length $$\ell$$. If it is displaced through a distance $$\ell$$ (from the lowest position) keeping the string straight, & then released. The speed of the bob at the lowest position is:

A ball of mass 3 kg collides with a wall with velocity $$10\:m/sec$$ at an angle of $$30^{\circ}$$ with the wall and after collision reflects at the same angle with the same speed. The change in momentum of ball in MKS unit is-

Two equal masses are attached to the two ends of a spring of spring constant k. The masses are pulled symmetrically to stretch the spring by a length x over its natural length. The work done by the spring on each mass during the pulling is

What is work done in holding a body of mass $$20\ kg$$ at a height of $$2\ m$$ above the ground? $$(g = 10\ m/s^2)$$

The velocity of a bus, moving on a smooth road, is increased from 8 m/s to 32 m/s in 120s. During this process, the potential energy of the bus

Two bodies P and Q of equal masses are kept at heights $$x$$ and $$4x$$ respectively. What will be the ratio of their potential energies?

Initially spring is relaxed. A person starts pulling the spring by applying  a variable force $$F$$. Find out the work done by $$F$$ to stretch it slowly to a distance by $$x$$.