## Conceptual Physics (12th Edition)

The work needed is the change in kinetic energy. Kinetic energy scales as the square of the speed, so if the speed is tripled, KE is multiplied by $3^{2} = 9$. The amount of stopping force multiplied by the distance is the KE, so for the same braking force, with 9 times the initial KE, the braking distance goes up by a factor of 9, from 15 m to 135 m. This is discussed on pages 114-115.