Edexcel M3 2016 January — Question 2

Exam BoardEdexcel
ModuleM3 (Mechanics 3)
Year2016
SessionJanuary
TopicNon-constant acceleration

2. A particle \(P\) is moving in a straight line. At time \(t\) seconds, the distance of \(P\) from a fixed point \(O\) on the line is \(x\) metres and the acceleration of \(P\) is \(( 6 - 2 t ) \mathrm { m } \mathrm { s } ^ { - 2 }\) in the direction of \(x\) increasing. When \(t = 0 , P\) is moving towards \(O\) with speed \(8 \mathrm {~m} \mathrm {~s} ^ { - 1 }\)
  1. Find the velocity of \(P\) in terms of \(t\).
  2. Find the total distance travelled by \(P\) in the first 4 seconds.