| Exam Board | Edexcel |
|---|---|
| Module | M2 (Mechanics 2) |
| Year | 2015 |
| Session | June |
| Marks | 11 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Variable acceleration (1D) |
| Type | Total distance with direction changes |
| Difficulty | Standard +0.3 This is a straightforward M2 mechanics question requiring standard techniques: (a) solving a quadratic equation when v=0, (b) differentiating velocity to find acceleration, (c) integrating velocity with attention to sign changes. While multi-part, each step uses routine methods with no novel insight required, making it slightly easier than average. |
| Spec | 3.02a Kinematics language: position, displacement, velocity, acceleration3.02f Non-uniform acceleration: using differentiation and integration |
\begin{enumerate}
\item A particle $P$ moves on the positive $x$-axis. The velocity of $P$ at time $t$ seconds is $\left( 2 t ^ { 2 } - 9 t + 4 \right) \mathrm { m } \mathrm { s } ^ { - 1 }$. When $t = 0 , P$ is 15 m from the origin $O$.
\end{enumerate}
Find\\
(a) the values of $t$ when $P$ is instantaneously at rest,\\
(b) the acceleration of $P$ when $t = 5$\\
(c) the total distance travelled by $P$ in the interval $0 \leqslant t \leqslant 5$
\hfill \mbox{\textit{Edexcel M2 2015 Q6 [11]}}