CAIE M1 2016 June — Question 7

Exam BoardCAIE
ModuleM1 (Mechanics 1)
Year2016
SessionJune
TopicNon-constant acceleration

7 A particle \(P\) moves in a straight line. At time \(t \mathrm {~s}\), the displacement of \(P\) from \(O\) is \(s \mathrm {~m}\) and the acceleration of \(P\) is \(a \mathrm {~m} \mathrm {~s} ^ { - 2 }\), where \(a = 6 t - 2\). When \(t = 1 , s = 7\) and when \(t = 3 , s = 29\).
  1. Find the set of values of \(t\) for which the particle is decelerating.
  2. Find \(s\) in terms of \(t\).
  3. Find the time when the velocity of the particle is \(10 \mathrm {~m} \mathrm {~s} ^ { - 1 }\).