Work Energy and...

A body of mass travels in a straight line with a velocity $$v=kx^{3/2}$$ where $$k$$ is a constant. The work done in displacing the body from $$x=0$$ to $$x$$ is proportional to:

A force $$\vec { F }=(3t\hat { i } +5\hat { j })$$N acts on a body due to which its position varies as $$\vec { S }=(2{t^2}\hat { i } -5\hat { j })$$. Find the work done by this force in initial $$2s$$.

A particle moves from origin to position $$\vec {r}_{1}=3\hat {i}+2\hat {j}-6\hat {k}$$ under the action of force $$4\hat {i}+\hat {j}+3\hat {k}N$$. the work done will be

A body of mass $$2kg$$ makes an elastic collision with another body at rest and comes to rest .The mass of the second body which collides with the first body is 

Under influence of a force $$\overrightarrow { F } \left( x \right) =\left( 3{ x }^{ 2 }-2x+5 \right) \hat { i } N$$ there is displacement of a particle from $$x=0$$ and $$x=5m$$ on $$x-$$axis. So work done is $$J$$.

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

An inclined track ends in a circular loop of diameter $$D$$. From what height on the track a particles should be released so that it completes that loop in the vertical plane?

A ball is dropped from certain height, after striking the gourn it rebounds till $$\frac{2}{5}th$$ of the initial height. The ration of its speed just before and just after striking the ground is [assume no loss of energy due to air friction]

A force acts on a $$30 gm$$ particle in such a way that the position of the particle as a function of time is given by $$x=3t-4{t}^{2}+{t}^{3}$$, where $$x$$ is in metres and $$t$$ is in seconds. The work done on the particle during the first $$4$$ second is  

A stone, tied at the end of a string $$80$$ cm long, is whirled in a horizontal circle with a constant speed. If the stone makes $$14$$ revolutions in $$25$$ sec, what is the magnitude of acceleration of the stone.