CAIE M2 2011 June — Question 4

Exam BoardCAIE
ModuleM2 (Mechanics 2)
Year2011
SessionJune
TopicNon-constant acceleration

4 A particle \(P\) starts from rest at a point \(O\) and travels in a straight line. The acceleration of \(P\) is \(( 15 - 6 x ) \mathrm { m } \mathrm { s } ^ { - 2 }\), where \(x \mathrm {~m}\) is the displacement of \(P\) from \(O\).
  1. Find the value of \(x\) for which \(P\) reaches its maximum velocity, and calculate this maximum velocity.
  2. Calculate the acceleration of \(P\) when it is at instantaneous rest and \(x > 0\).