9 In an experiment, a small box is hit across a floor. After it has been hit, the box slides without rotation.
The box passes a point A. The distance the box travels after passing A before coming to rest is \(S\) metres and the time this takes is \(T\) seconds.
The only resistance to the box's motion is friction due to the floor. The mass of the box is \(m \mathrm {~kg}\) and the frictional force is a constant \(F\).
- Find the equation of motion for the box while it is sliding.
- Show that \(S = k T ^ { 2 }\) where \(k = \frac { F } { 2 m }\).
- Given that \(k = 1.4\), find the value of the coefficient of friction between the box and the floor.