Moderate -0.3 This is a straightforward mechanics question requiring differentiation to find acceleration, solving a linear equation for time, then integration to find displacement. All steps are routine applications of standard techniques with no conceptual challenges, making it slightly easier than average.
2 A particle starts at a point \(O\) and moves along a straight line. Its velocity \(t\) s after leaving \(O\) is \(\left( 1.2 t - 0.12 t ^ { 2 } \right) \mathrm { m } \mathrm { s } ^ { - 1 }\). Find the displacement of the particle from \(O\) when its acceleration is \(0.6 \mathrm {~m} \mathrm {~s} ^ { - 2 }\).
2 A particle starts at a point $O$ and moves along a straight line. Its velocity $t$ s after leaving $O$ is $\left( 1.2 t - 0.12 t ^ { 2 } \right) \mathrm { m } \mathrm { s } ^ { - 1 }$. Find the displacement of the particle from $O$ when its acceleration is $0.6 \mathrm {~m} \mathrm {~s} ^ { - 2 }$.
\hfill \mbox{\textit{CAIE M1 2010 Q2 [5]}}