| Exam Board | Edexcel |
|---|---|
| Module | M1 (Mechanics 1) |
| Year | 2007 |
| Session | June |
| Marks | 11 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Travel graphs |
| Type | Velocity-time graph sketching |
| Difficulty | Moderate -0.8 This is a straightforward SUVAT problem requiring students to sketch a velocity-time graph and use the area-under-graph method to find unknown values. The multi-stage motion is clearly described, requiring only standard techniques (trapezium area formula and basic kinematics) with no conceptual challenges or novel problem-solving—easier than average for M1. |
| Spec | 3.02b Kinematic graphs: displacement-time and velocity-time3.02d Constant acceleration: SUVAT formulae |
| Answer | Marks | Guidance |
|---|---|---|
| (a) 2 horizontal lines | B1 | (3 marks) |
| Joined by straight line sloping down | B1 | |
| 25, 10, 18, 30 or similar | B1 | |
| (b) \(25 \times 10 + \frac{1}{2}(25 + V) \times 8 + 12 \times V = 526\) | M1 A1 A1 | (5 marks) |
| Solving to \(V = 11\) | DM1 A1 | |
| (c) \(v = u + at\) ⟹ \(11 = 25 - 8a\) | M1 A1ft | (3 marks) |
| \(a = 1.75\) (ms⁻²) | A1 | |
| [11] |
**(a)** 2 horizontal lines | B1 | (3 marks)
Joined by straight line sloping down | B1 |
25, 10, 18, 30 or similar | B1 |
**(b)** $25 \times 10 + \frac{1}{2}(25 + V) \times 8 + 12 \times V = 526$ | M1 A1 A1 | (5 marks)
Solving to $V = 11$ | DM1 A1 |
**(c)** $v = u + at$ ⟹ $11 = 25 - 8a$ | M1 A1ft | (3 marks)
$a = 1.75$ (ms⁻²) | A1 |
| | [11] |\begin{enumerate}
\item A car is moving along a straight horizontal road. At time $t = 0$, the car passes a point $A$ with speed $25 \mathrm {~m} \mathrm {~s} ^ { - 1 }$. The car moves with constant speed $25 \mathrm {~m} \mathrm {~s} ^ { - 1 }$ until $t = 10 \mathrm {~s}$. The car then decelerates uniformly for 8 s . At time $t = 18 \mathrm {~s}$, the speed of the car is $V \mathrm {~m} \mathrm {~s} ^ { - 1 }$ and this speed is maintained until the car reaches the point $B$ at time $t = 30 \mathrm {~s}$.\\
(a) Sketch, in the space below, a speed-time graph to show the motion of the car from $A$ to $B$.
\end{enumerate}
Given that $A B = 526 \mathrm {~m}$, find\\
(b) the value of $V$,\\
(c) the deceleration of the car between $t = 10 \mathrm {~s}$ and $t = 18 \mathrm {~s}$.
\hfill \mbox{\textit{Edexcel M1 2007 Q4 [11]}}