Moderate -0.3 This is a straightforward M2 integration question requiring students to integrate a linear acceleration function and apply initial conditions. While it involves non-constant acceleration (making it M2 rather than M1), the integration itself is routine (polynomial), and finding T requires only solving a simple quadratic equation. Slightly easier than average due to its direct application of standard technique.
1 A particle P moves on the x-axis. The acceleration of P at time t seconds, \(\mathrm { t } \geqslant 0\), is \(( 3 \mathrm { t } + 5 ) \mathrm { ms } ^ { - 2 }\) in the positive x -direction. When \(\mathrm { t } = 0\), the velocity of P is \(2 \mathrm {~ms} ^ { - 1 }\) in the positive x -direction. When \(\mathrm { t } = \mathrm { T }\), the velocity of P is \(6 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) in the positive x -direction. Find the value of T .
(6)
1 A particle P moves on the x-axis. The acceleration of P at time t seconds, $\mathrm { t } \geqslant 0$, is $( 3 \mathrm { t } + 5 ) \mathrm { ms } ^ { - 2 }$ in the positive x -direction. When $\mathrm { t } = 0$, the velocity of P is $2 \mathrm {~ms} ^ { - 1 }$ in the positive x -direction. When $\mathrm { t } = \mathrm { T }$, the velocity of P is $6 \mathrm {~m} \mathrm {~s} ^ { - 1 }$ in the positive x -direction. Find the value of T .\\
(6)
\hfill \mbox{\textit{Edexcel M2 Q1 [6]}}