| Exam Board | Edexcel |
|---|---|
| Module | M2 (Mechanics 2) |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Variable acceleration (1D) |
| Type | Velocity from displacement differentiation |
| Difficulty | Moderate -0.8 This is a straightforward kinematics question requiring only routine differentiation and algebraic manipulation. Part (a) involves showing x>0 for t>0 (trivial), part (b) is direct differentiation and solving a linear equation, and part (c) requires differentiating twice to find constant acceleration then applying F=ma. All techniques are standard M2 procedures with no problem-solving insight required, making it easier than average but not trivial due to the multi-part structure. |
| Spec | 3.02f Non-uniform acceleration: using differentiation and integration3.03c Newton's second law: F=ma one dimension |
| Answer | Marks | Guidance |
|---|---|---|
| (a) When \(x = 0\), \(t(3t + 8) = 0\) | M1 A1 | No solution for \(t > 0\) |
| (b) \(v = 6t + 8\) | M1 A1 A1 | When \(v = 20\), \(6t = 12\), so \(t = 2\) |
| (c) \(a = 6\), constant | B1 M1 A1 | \(F = 0.4 \times 6 = 2.4 \text{ N}\) |
**(a)** When $x = 0$, $t(3t + 8) = 0$ | M1 A1 | No solution for $t > 0$
**(b)** $v = 6t + 8$ | M1 A1 A1 | When $v = 20$, $6t = 12$, so $t = 2$
**(c)** $a = 6$, constant | B1 M1 A1 | $F = 0.4 \times 6 = 2.4 \text{ N}$
**Total: 8 marks**
---A particle $P$, of mass 0.4 kg, moves in a straight line such that, at time $t$ seconds after passing through a fixed point $O$, its distance from $O$ is $x$ metres, where $x = 3t^2 + 8t$.
\begin{enumerate}[label=(\alph*)]
\item Show that $P$ never returns to $O$. [2 marks]
\item Find the value of $t$ when $P$ has velocity 20 ms$^{-1}$. [3 marks]
\item Show that the force acting on $P$ is constant, and find its magnitude. [3 marks]
\end{enumerate}
\hfill \mbox{\textit{Edexcel M2 Q3 [8]}}