Standard +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.
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 \(t = 2\).
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]}}