| Exam Board | Edexcel |
|---|---|
| Module | M1 (Mechanics 1) |
| Year | 2004 |
| Session | November |
| Marks | 10 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Vectors Introduction & 2D |
| Type | Velocity from acceleration and initial conditions |
| Difficulty | Moderate -0.8 This is a straightforward M1 mechanics question testing basic vector kinematics with constant acceleration. Part (a) requires simple angle calculation using tan^(-1), part (b) uses v = u + at directly, part (c) applies Pythagoras to find speed, and part (d) sets the j-component to zero. All parts are routine applications of standard formulas with no problem-solving insight required, making it easier than average. |
| Spec | 1.10c Magnitude and direction: of vectors1.10h Vectors in kinematics: uniform acceleration in vector form3.03d Newton's second law: 2D vectors |
A particle $P$ moves in a horizontal plane. The acceleration of $P$ is $(-\mathbf{i} + 2\mathbf{j}) \text{ m s}^{-2}$. At time $t = 0$, the velocity of $P$ is $(2\mathbf{i} - 3\mathbf{j}) \text{ m s}^{-1}$.
\begin{enumerate}[label=(\alph*)]
\item Find, to the nearest degree, the angle between the vector $\mathbf{j}$ and the direction of motion of $P$ when $t = 0$. [3]
\end{enumerate}
At time $t$ seconds, the velocity of $P$ is $\mathbf{v} \text{ m s}^{-1}$. Find
\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{1}
\item an expression for $\mathbf{v}$ in terms of $t$, in the form $a\mathbf{i} + b\mathbf{j}$, [2]
\item the speed of $P$ when $t = 3$, [3]
\item the time when $P$ is moving parallel to $\mathbf{i}$. [2]
\end{enumerate}
\hfill \mbox{\textit{Edexcel M1 2004 Q5 [10]}}