CAIE FP2 2017 November — Question 1 4 marks

Exam BoardCAIE
ModuleFP2 (Further Pure Mathematics 2)
Year2017
SessionNovember
Marks4
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TopicCircular Motion 1
TypeRadial and transverse acceleration
DifficultyStandard +0.3 This is a straightforward application of circular motion formulas requiring students to recognize that transverse acceleration equals dv/dt, set it to zero at t=2 to find p, then calculate radial acceleration v²/r. While it involves Further Maths content, the problem-solving is mechanical with clear steps and standard formulas.
Spec6.05e Radial/tangential acceleration

1 A particle \(P\) is moving in a circle of radius 0.8 m . At time \(t \mathrm {~s}\) its velocity is \(\left( 8 - p t + t ^ { 2 } \right) \mathrm { m } \mathrm { s } ^ { - 1 }\), where \(p\) is a constant. The magnitude of the transverse component of the acceleration of \(P\) when \(t = 2\) is zero. Find the magnitude of the radial component of the acceleration of \(P\) when \(t = 2\).

Question 1:
AnswerMarks Guidance
AnswerMarks Guidance
\(-p + 2t = 0,\ p = 4\)M1 A1 Find \(p\) by equating transverse acceleration to 0 at \(t = 2\)
\(a_R = (8 - pt + t^2)^2 / 0.8\)M1 Find radial acceleration \(a_R\) at \(t = 2\) in terms of \(p\) from \(v^2/r\)
\(= 4^2 / 0.8 = 20\ \text{ms}^{-2}\)A1 Evaluate with \(p = 4\)
4
# Question 1:

| Answer | Marks | Guidance |
|--------|-------|----------|
| $-p + 2t = 0,\ p = 4$ | **M1 A1** | Find $p$ by equating transverse acceleration to 0 at $t = 2$ |
| $a_R = (8 - pt + t^2)^2 / 0.8$ | **M1** | Find radial acceleration $a_R$ at $t = 2$ in terms of $p$ from $v^2/r$ |
| $= 4^2 / 0.8 = 20\ \text{ms}^{-2}$ | **A1** | Evaluate with $p = 4$ |
| | **4** | |
1 A particle $P$ is moving in a circle of radius 0.8 m . At time $t \mathrm {~s}$ its velocity is $\left( 8 - p t + t ^ { 2 } \right) \mathrm { m } \mathrm { s } ^ { - 1 }$, where $p$ is a constant. The magnitude of the transverse component of the acceleration of $P$ when $t = 2$ is zero. Find the magnitude of the radial component of the acceleration of $P$ when $t = 2$.\\

\hfill \mbox{\textit{CAIE FP2 2017 Q1 [4]}}