| Exam Board | Edexcel |
|---|---|
| Module | M1 (Mechanics 1) |
| Year | 2007 |
| Session | January |
| Marks | 10 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Variable acceleration (1D) |
| Type | Displacement from velocity by integration |
| Difficulty | Moderate -0.8 This is a straightforward application of SUVAT equations for constant acceleration under gravity. All three parts use standard kinematic formulas with clearly defined initial conditions, requiring only direct substitution and basic algebraic manipulation. While it's a multi-part question worth 10 marks total, each part follows a routine textbook pattern with no problem-solving insight needed, making it easier than the average A-level question. |
| Spec | 3.02d Constant acceleration: SUVAT formulae3.02h Motion under gravity: vector form |
| Answer | Marks | Guidance |
|---|---|---|
| (a) \(v^2 = u^2 + 2as ⇒ 0^2 = 21^2 - 2 \times 9.8 \times h\) → \(h = 22.5\) (m) | M1 A1 | 3 marks |
| (b) \(v^2 = u^2 + 2as ⇒ v^2 = 0^2 + 2 \times 9.8 \times 24\) (\(= 470.4\)) → \(v ≈ 22\) (m s\(^{-1}\)) | M1 A1 | accept 21.7 |
| (c) \(v = u + at ⇒ -\sqrt{470.4} = 21 - 9.8t\) or equivalent | M1 A2(1,0) | –1 each error |
**(a)** $v^2 = u^2 + 2as ⇒ 0^2 = 21^2 - 2 \times 9.8 \times h$ → $h = 22.5$ (m) | M1 A1 | 3 marks
**(b)** $v^2 = u^2 + 2as ⇒ v^2 = 0^2 + 2 \times 9.8 \times 24$ ($= 470.4$) → $v ≈ 22$ (m s$^{-1}$) | M1 A1 | accept 21.7 | 3 marks
**(c)** $v = u + at ⇒ -\sqrt{470.4} = 21 - 9.8t$ or equivalent | M1 A2(1,0) | –1 each error | → $t ≈ 4.4$ (s) | A1 | accept 4.36 | 4 marks | 10 marks total
---A ball is projected vertically upwards with speed 21 m s$^{-1}$ from a point $A$, which is 1.5 m above the ground. After projection, the ball moves freely under gravity until it reaches the ground. Modelling the ball as a particle, find
\begin{enumerate}[label=(\alph*)]
\item the greatest height above $A$ reached by the ball, [3]
\item the speed of the ball as it reaches the ground, [3]
\item the time between the instant when the ball is projected from $A$ and the instant when the ball reaches the ground. [4]
\end{enumerate}
\hfill \mbox{\textit{Edexcel M1 2007 Q5 [10]}}