Work Energy and...

A $$110 kg$$ panda is riding on a $$3.0 m$$ long swing whose mass can be considered negligible. The highest point of its arc occurs when the swing makes a $${20}^{o}$$ angle with the vertical.
What is the magnitude of the total tension in the ropes of the swing at that point?

The correct formula to find the velocity of a body with kinetic energy '$$k$$' is:

The position function of a particle is given by $$x\left(t\right)=k{t}^{{5}/{2}}$$, where $$k$$ is a constant.
If the particle starts at rest and is propelled through some distance $$d$$ so that the trajectory matches $$x\left(t\right)$$, the work done on the particle is proportional to which power of $$t$$?

A body is acted upon by a force which is proportional to the distance covered. If distance covered by denoted by x, then work done by the force will be proportional to:

A small stone tied to an inextensible string of negligible mass is rotated in a circle of radius $$2 m$$ in a vertical plane. Find the speed at a horizontal point on the circle. (in $$m/s$$)

A stone of mass $$10 kg$$ tied with a string of length $$0.5 m$$ is rotated in a vertical circle. Find the total energy of the stone at the highest position. (in $$J$$)

Under the action of a force $$F=Cx$$, the position of a body changes from $$0$$ to $$x$$. The work done is :

A $$2kg$$ object is moving at $$3m/s$$. A $$4N$$ force is applied in the direction of motion and then removed after the object has travelled an additional $$5m$$. The work done by this force is:

Calculate the work done in moving a cart from $$x=a$$ to $$x=b$$ whose mass is $$3kg$$ and the given surface is frictionless. $$(Take\ g=9.8m/s^{2})$$

A $$200 g$$ mass is whirled in a vertical circle making $$60$$ revolutions per minute. What is the tension in the string at the top of the circle if the radius of the circle is $$0.8 m$$? (in $$N$$)