Moderate -0.8 This is a straightforward integration problem requiring one integration of acceleration to find velocity, applying initial conditions, then solving a simple quadratic equation. It's a standard M2 exercise with clear setup and routine calculus, making it easier than average but not trivial due to the algebraic manipulation required.
A particle \(P\) moves on the \(x\)-axis. The acceleration of \(P\) at time \(t\) seconds, \(t \geq 0\), is \((3t + 5)\) m s\(^{-2}\) in the positive \(x\)-direction. When \(t = 0\), the velocity of \(P\) is 2 m s\(^{-1}\) in the positive \(x\)-direction. When \(t = T\), the velocity of \(P\) is 6 m s\(^{-1}\) in the positive \(x\)-direction. Find the value of \(T\).
(6)
A particle $P$ moves on the $x$-axis. The acceleration of $P$ at time $t$ seconds, $t \geq 0$, is $(3t + 5)$ m s$^{-2}$ in the positive $x$-direction. When $t = 0$, the velocity of $P$ is 2 m s$^{-1}$ in the positive $x$-direction. When $t = T$, the velocity of $P$ is 6 m s$^{-1}$ in the positive $x$-direction. Find the value of $T$.
(6)
\hfill \mbox{\textit{Edexcel M2 2010 Q1}}