| Exam Board | Edexcel |
|---|---|
| Module | M1 (Mechanics 1) |
| Year | 2014 |
| Session | June |
| Marks | 13 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Constant acceleration (SUVAT) |
| Type | Multi-phase journey: find unknown speed or time |
| Difficulty | Moderate -0.3 This is a straightforward multi-stage SUVAT question where all accelerations and times are given explicitly. Students apply v=u+at and s=ut+½at² systematically to each stage with no problem-solving required beyond careful bookkeeping. The structure is standard for M1, though the multiple stages and final distance constraint add minor computational complexity above the most basic exercises. |
| Spec | 3.02d Constant acceleration: SUVAT formulae |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| \(v_1 = 8 \times 1.5\ (=12)\) | M1 | Use of \(v = u + at\) or equivalent for \(t = 8\) |
| \(v_2 = 12 + 0.8 \times 20\) | M1 | Follow their 12 |
| \(v_2 = 28\) m s\(^{-1}\) | A1(3) |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| Correct shape (trapezium with triangle at start) | B1 | Shape |
| Numbers 8, 28; 12, 28 indicated | B1ft(2) | nos: 8,28; 12,28 indicated. Follow their 12, 28 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| First 8 s: dist \(= \frac{1}{2} \times 8 \times 12\ (= 48)\) | M1 | Correct method for distance for the triangle (0-8) or the trapezium (8-28) |
| A1ft | Follow their 12 | |
| Next 20 s: dist \(= \frac{1}{2}(12+28) \times 20\ (= 400)\) | A1ft | Follow their 12, 28 |
| Total dist \(= 448\) m | A1(4) | Correct answer only (cao) |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| \(0 = 28^2 - 2 \times 2.8s\) | M1 | Find area of right hand triangle or an expression in \(T\) for the trapezium (rectangle + triangle) |
| \(s = \frac{28^2}{2 \times 2.8}\ (= 140)\) | A1ft | Follow their 28 |
| \(448 + 140 + 28T = 2000\) | DM1 | Form an equation in \(T\) for their 16, 448 and 140 |
| \(T = \frac{2000 - 448 - 140}{28} = 50.4\) | A1(4) | Or better (50.42857...) Accept 50 |
# Question 6:
## Part (a):
| Answer | Marks | Guidance |
|--------|-------|----------|
| $v_1 = 8 \times 1.5\ (=12)$ | M1 | Use of $v = u + at$ or equivalent for $t = 8$ |
| $v_2 = 12 + 0.8 \times 20$ | M1 | Follow their 12 |
| $v_2 = 28$ m s$^{-1}$ | A1(3) | |
## Part (b):
| Answer | Marks | Guidance |
|--------|-------|----------|
| Correct shape (trapezium with triangle at start) | B1 | Shape |
| Numbers 8, 28; 12, 28 indicated | B1ft(2) | nos: 8,28; 12,28 indicated. Follow their 12, 28 |
## Part (c):
| Answer | Marks | Guidance |
|--------|-------|----------|
| First 8 s: dist $= \frac{1}{2} \times 8 \times 12\ (= 48)$ | M1 | Correct method for distance for the triangle (0-8) or the trapezium (8-28) |
| | A1ft | Follow their 12 |
| Next 20 s: dist $= \frac{1}{2}(12+28) \times 20\ (= 400)$ | A1ft | Follow their 12, 28 |
| Total dist $= 448$ m | A1(4) | Correct answer only (cao) |
## Part (d):
| Answer | Marks | Guidance |
|--------|-------|----------|
| $0 = 28^2 - 2 \times 2.8s$ | M1 | Find area of right hand triangle or an expression in $T$ for the trapezium (rectangle + triangle) |
| $s = \frac{28^2}{2 \times 2.8}\ (= 140)$ | A1ft | Follow their 28 |
| $448 + 140 + 28T = 2000$ | DM1 | Form an equation in $T$ for their 16, 448 and 140 |
| $T = \frac{2000 - 448 - 140}{28} = 50.4$ | A1(4) | Or better (50.42857...) Accept 50 |
**Total: [13]**
---\begin{enumerate}
\item A car starts from rest at a point $A$ and moves along a straight horizontal road. The car moves with constant acceleration $1.5 \mathrm {~m} \mathrm {~s} ^ { - 2 }$ for the first 8 s . The car then moves with constant acceleration $0.8 \mathrm {~m} \mathrm {~s} ^ { - 2 }$ for the next 20 s . It then moves with constant speed for $T$ seconds before slowing down with constant deceleration $2.8 \mathrm {~m} \mathrm {~s} ^ { - 2 }$ until it stops at a point $B$.\\
(a) Find the speed of the car 28 s after leaving $A$.\\
(b) Sketch, in the space provided, a speed-time graph to illustrate the motion of the car as it travels from $A$ to $B$.\\
(c) Find the distance travelled by the car during the first 28 s of its journey from $A$.
\end{enumerate}
The distance from $A$ to $B$ is 2 km .\\
(d) Find the value of $T$.\\
\hfill \mbox{\textit{Edexcel M1 2014 Q6 [13]}}