CAIE Further Paper 3 2020 June — Question 2

Exam BoardCAIE
ModuleFurther Paper 3 (Further Paper 3)
Year2020
SessionJune
TopicFirst order differential equations (integrating factor)

2 A particle \(Q\) of mass \(m \mathrm {~kg}\) falls from rest under gravity. The motion of \(Q\) is resisted by a force of magnitude \(m k v \mathrm {~N}\), where \(v \mathrm {~ms} ^ { - 1 }\) is the speed of \(Q\) at time \(t \mathrm {~s}\) and \(k\) is a positive constant. Find an expression for \(v\) in terms of \(g , k\) and \(t\).