Edexcel M3 2004 June — Question 3

Exam BoardEdexcel
ModuleM3 (Mechanics 3)
Year2004
SessionJune
TopicVariable Force

3. A particle \(P\) of mass \(m \mathrm {~kg}\) slides from rest down a smooth plane inclined at \(30 ^ { \circ }\) to the horizontal. When \(P\) has moved a distance \(x\) metres down the plane, the resistance to the motion of \(P\) from non-gravitational forces has magnitude \(m x ^ { 2 }\) newtons. Find
  1. the speed of \(P\) when \(x = 2\),
  2. the distance \(P\) has moved when it comes to rest for the first time.