A 70 kg bicyclist rides his 9.8 kg bicycle with a speed of 16 m/s.
How much work must be done by the brakes to bring the bike and rider to a stop?

Hello,

✔ We have Ek = 1/2m x v²

In order to come to a complete stop, the cyclist must convert all his kinetic energy into thermal energy. Given that the braking force opposes movement, the work is therefore resistant, i.e.  W = -10 214.4 J.

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 .