OCR M1 Specimen — Question 5

Exam BoardOCR
ModuleM1 (Mechanics 1)
SessionSpecimen
TopicNon-constant acceleration

5 A particle \(P\) moves in a straight line so that, at time \(t\) seconds after leaving a fixed point \(O\), its acceleration is \(- \frac { 1 } { 10 } t \mathrm {~m} \mathrm {~s} ^ { - 2 }\). At time \(t = 0\), the velocity of \(P\) is \(V \mathrm {~m} \mathrm {~s} ^ { - 1 }\).
  1. Find, by integration, an expression in terms of \(t\) and \(V\) for the velocity of \(P\).
  2. Find the value of \(V\), given that \(P\) is instantaneously at rest when \(t = 10\).
  3. Find the displacement of \(P\) from \(O\) when \(t = 10\).
  4. Find the speed with which the particle returns to \(O\).