| Exam Board | Edexcel |
|---|---|
| Module | M1 (Mechanics 1) |
| Marks | 12 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Forces, equilibrium and resultants |
| Type | Particle on inclined plane |
| Difficulty | Standard +0.3 This is a standard M1 mechanics question requiring Newton's second law on an incline (part a) and kinematics with uniform acceleration (part b). Both parts use routine techniques taught in M1 with straightforward application of formulas, though part (b) requires careful interpretation of 'fifth second' and multi-step working. Slightly easier than average due to the standard nature of both components. |
| Spec | 3.02d Constant acceleration: SUVAT formulae3.03c Newton's second law: F=ma one dimension3.03f Weight: W=mg |
| Answer | Marks | Guidance |
|---|---|---|
| \(a = 0.43\), ∴ decel. = \(0.43\) ms\(^{-2}\) (2dp) | M1 A1 | M1 A1 |
| Answer | Marks | Guidance |
|---|---|---|
| \(v = 3 + 2 \times 5 = 13\) ms\(^{-1}\) | M1 | M1 A1 |
**(a)** resolve // to plane: $50 - 20 - 70\sin 5° = 70a$
$a = 0.43$, ∴ decel. = $0.43$ ms$^{-2}$ (2dp) | M1 A1 | M1 A1 |
**(b)** use of $s = ut + \frac{1}{4}at^2$ with $u = 3$ for $t = 4$ and $t = 5$
to give $s = 12 + 8a$ and $s = 15 + 12.5a$
∴ $15 + 12.5a = 12 + 8a + 12$
$4.5a = 9$ ∴ $a = 2$
use $v = u + at$ with $u = 3, a = 2, t = 5$
$v = 3 + 2 \times 5 = 13$ ms$^{-1}$ | M1 | M1 A1 | M1 | M1 A1 | M1 | A1 | (12) |
---A cyclist is riding up a hill inclined at an angle of 5° to the horizontal. She produces a driving force of 50 N and experiences resistive forces which total 20 N.
Given that the combined mass of the cyclist and her bicycle is 70 kg,
\begin{enumerate}[label=(\alph*)]
\item find, correct to 2 decimal places, the magnitude of the deceleration of the cyclist. [4 marks]
\end{enumerate}
When the cyclist reaches the top of the hill, her speed is 3 m s$^{-1}$. She subsequently accelerates uniformly so that in the fifth second after she has reached the top of the hill, she travels 12 m.
\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{1}
\item Find her speed at the end of the fifth second. [8 marks]
\end{enumerate}
\hfill \mbox{\textit{Edexcel M1 Q5 [12]}}