CAIE M1 2024 June — Question 2

Exam BoardCAIE
ModuleM1 (Mechanics 1)
Year2024
SessionJune
TopicNon-constant acceleration

2 A particle \(P\) moves in a straight line. At time \(t\) s after leaving a point \(O\) on the line, \(P\) has velocity \(v \mathrm {~ms} ^ { - 1 }\), where \(\mathrm { v } = 44 \mathrm { t } - 6 \mathrm { t } ^ { 2 } - 36\).
  1. Find the set of values of \(t\) for which the acceleration of the particle is positive.
  2. Find the two values of \(t\) at which \(P\) returns to \(O\).
    \includegraphics[max width=\textwidth, alt={}, center]{3eaf3652-ff91-4bae-9f20-83487d635612-04_714_796_248_635} Four coplanar forces of magnitude \(P \mathrm {~N} , 10 \mathrm {~N} , 16 \mathrm {~N}\) and 2 N act at a point in the directions shown in the diagram. It is given that the forces are in equilibrium. Find the values of \(\theta\) and \(P\).