| Exam Board | Edexcel |
|---|---|
| Module | M2 (Mechanics 2) |
| Year | 2015 |
| Session | June |
| Marks | 10 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Variable acceleration (1D) |
| Type | Vector motion with components |
| Difficulty | Standard +0.3 This is a straightforward M2 mechanics question requiring standard techniques: differentiation to find acceleration, solving when j-component of velocity equals zero, then integration with initial conditions to find position. While it involves vectors and multiple steps, each step follows routine procedures with no novel problem-solving required, making it slightly easier than average. |
| Spec | 1.08d Evaluate definite integrals: between limits1.10h Vectors in kinematics: uniform acceleration in vector form3.02f Non-uniform acceleration: using differentiation and integration |
| Answer | Marks |
|---|---|
| 2(a) | B1 for t = 2 |
| Answer | Marks |
|---|---|
| 2(b) | First M1 for attempt to integrate (at least one power increasing by 1) and |
Question 2:
--- 2(a) ---
2(a) | B1 for t = 2
First M1 for attempt to differentiate (at least one power decreasing by 1)
and i and j included
First A1 for correct expression
Second M1 for putting their t (≠ 0) value in their vector a, which must
contain i’s and j’s, AND using Pythag with sq root
Second A1 for √288 or 17 or better
--- 2(b) ---
2(b) | First M1 for attempt to integrate (at least one power increasing by 1) and
i and j included
First A1 for correct expression with or without C
Second M1 for using t = 1 and -5i + 2j, in their vector r to obtain a
complete vector expression for r at time t
Second A1 for a correct expression (i’s and j’s do not need to be
collected)
Third A1 for 23i – 2j.At time $t$ seconds, $t \geq 0$, a particle $P$ has velocity $\mathbf{v}$ m s$^{-1}$, where
$$\mathbf{v} = (27 - 3t^2)\mathbf{i} + (8 - t^3)\mathbf{j}$$
When $t = 1$, the particle $P$ is at the point with position vector $\mathbf{r}$ m relative to a fixed origin $O$, where $\mathbf{r} = -5\mathbf{i} + 2\mathbf{j}$
Find
\begin{enumerate}[label=(\alph*)]
\item the magnitude of the acceleration of $P$ at the instant when it is moving in the direction of the vector $\mathbf{i}$, [5]
\item the position vector of $P$ at the instant when $t = 3$ [5]
\end{enumerate}
\hfill \mbox{\textit{Edexcel M2 2015 Q2 [10]}}