Standard +0.3 This is a straightforward application of circular motion formulas requiring calculation of tangential acceleration (differentiation of velocity) and radial acceleration (v²/r), then combining using Pythagoras. The algebra is simple with given values, making it slightly easier than average despite being Further Maths content.
1 A particle is moving in a circle of radius 2 m . At time \(t \mathrm {~s}\) its velocity is \(\left( t ^ { 2 } - 12 \right) \mathrm { m } \mathrm { s } ^ { - 1 }\). Find the magnitude of the resultant acceleration of the particle when \(t = 4\).
1 A particle is moving in a circle of radius 2 m . At time $t \mathrm {~s}$ its velocity is $\left( t ^ { 2 } - 12 \right) \mathrm { m } \mathrm { s } ^ { - 1 }$. Find the magnitude of the resultant acceleration of the particle when $t = 4$.
\hfill \mbox{\textit{CAIE FP2 2011 Q1 [4]}}