The work-energy theorem states that Work = Change in Kinetic Energy. A 5.0 kg crate is moving at 5.0 m/s. How much work would be needed to increase the speed to 10.0 m/s?

no. dot product   =0 when vecs at right angles

we have been given a quadratic function and we need to restrict the domain such that it becomes a one to one function.

we know that vertex of this quadratic function occurs at (5,2).

further, we know that range of this function is .

if we restrict the domain of this function to either or , it will become one to one function.

let us know find its inverse.

upon interchanging x and y, we get:

let us now solve this function for y.

hence, the inverse function would be if we restrict the domain of original function to and the inverse function would be if we restrict the domain to .

force required to detach it is given by

charges are taken to be fundamental charge

now we have

so above is the minimum distance at which it will detach