1 A particle moves up a line of greatest slope of a rough plane inclined at an angle \(\alpha\) to the horizontal, where \(\sin \alpha = 0.28\). The coefficient of friction between the particle and the plane is \(\frac { 1 } { 3 }\).

1. Show that the acceleration of the particle is \(- 6 \mathrm {~m} \mathrm {~s} ^ { - 2 }\).
2. Given that the particle's initial speed is \(5.4 \mathrm {~m} \mathrm {~s} ^ { - 1 }\), find the distance that the particle travels up the plane.