Work Energy and...

A particle moves under the effect of a force $$F=Cx$$ from $$x=0$$ to $$x={x}_{1}$$. The work done in the process is

A force acts on a $$3\ g$$ 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 second. The work done during the first $$4$$ second  is:

Two particles of masses $${m}_{1}$$ and $${m}_{2}$$ in projectile motion have velocities $${v}_{1}$$ and $${v}_{2}$$ respectively at time $$t=0$$. They collide at time $${t}_{0}$$. Their velocities become $${v'}_{1}$$ and $${v'}_{2}$$ at time $$2{t}_{0}$$ while still moving in air. The value of $$\left[ \left( { m }_{ 1 }{ v' }_{ 1 }+{ m }_{ 2 }{ v' }_{ 2 } \right) -\left( { m }_{ 1 }{ v }_{ 1 }+{ m }_{ 2 }{ v }_{ 2 } \right)  \right] $$

A stone of mass $$0.2kg$$ is tied to one end of a thread of length $$0.1m$$ whirled in a vertical circle. When the stone is at the lowest point of circle, tension in thread is $$52N$$, then velocity of the stone will be:

A stone of mass $$1kg$$ is tied to the end of a string of $$1m$$ length. It is whirled in a vertical circle. If the velocity of the stone at the top be $$4m/s$$. What is the tension in the string (at that instant)?

Force constant of spring one is $$K$$ and another spring is $$2K$$. When both spring are stretched through same distance, then the work done

A particle of mass $$m$$ initially moving with speed $$v$$. A force acts on the particle $$f=kx$$ where $$x$$ is the distance travelled by the particle and $$k$$ is constant. Find the speed of the particle when the work done by the force equals $$W$$.

A wheel rotating at an angular speed of 20 rad$${ s }^{ -1 }$$, is brought to rest by a constant torque in 4s.If the M.I is 0.2 kg $${ m }^{ 2 }$$, the work done in first 2s is:

A force of $$(4{ x }^{ 2 }+3x)N$$ acts on a particle which displaces it from $$x=2m$$ to $$x=3m$$. The work done by the force is:

A force of $$(4x^{2}+3x)\ N$$ acts on a particle which displaces it from $$x=2m$$ to $$x=3m$$. Te work done by the force is: