| Exam Board | Edexcel |
|---|---|
| Module | M1 (Mechanics 1) |
| Year | 2008 |
| Session | June |
| Marks | 9 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Travel graphs |
| Type | Velocity-time graph sketching |
| Difficulty | Moderate -0.8 This is a straightforward M1 kinematics question requiring a standard velocity-time graph sketch and a single calculation using the trapezium area formula to find deceleration. The problem clearly states all phases of motion and requires only basic algebraic manipulation, making it easier than average for A-level. |
| Spec | 3.02b Kinematic graphs: displacement-time and velocity-time3.02d Constant acceleration: SUVAT formulae |
| Answer | Marks | Guidance |
|---|---|---|
| (a) Graph shape: straight line at \(v = 25\) until \(t = 30\), then straight line decreasing to \(v = 10\) at \(t = 90\) | B1 B1 | (2) |
| Answer | Marks | Guidance |
|---|---|---|
| (b) \(30 \times 25 + \frac{1}{2}(25 + 10) \times 10 + (60 - t) \times 10 = 1410\) giving \(7.5t = 60\) so \(t = 8 \text{ (s)}\) and \(a = \frac{25-10}{8} = 1.875 \text{ (ms}^{-2})\) | M1 A1 A1 DM1 A1 | \(1\frac{7}{8}\) M1 A1 |
**(a)** Graph shape: straight line at $v = 25$ until $t = 30$, then straight line decreasing to $v = 10$ at $t = 90$ | B1 B1 | (2)
Values: 25, 10, 30, 90
**(b)** $30 \times 25 + \frac{1}{2}(25 + 10) \times 10 + (60 - t) \times 10 = 1410$ giving $7.5t = 60$ so $t = 8 \text{ (s)}$ and $a = \frac{25-10}{8} = 1.875 \text{ (ms}^{-2})$ | M1 A1 A1 DM1 A1 | $1\frac{7}{8}$ M1 A1 | (7) [9]
---4. A car is moving along a straight horizontal road. The speed of the car as it passes the point $A$ is $25 \mathrm {~m} \mathrm {~s} ^ { - 1 }$ and the car maintains this speed for 30 s . The car then decelerates uniformly to a speed of $10 \mathrm {~m} \mathrm {~s} ^ { - 1 }$. The speed of $10 \mathrm {~m} \mathrm {~s} ^ { - 1 }$ is then maintained until the car passes the point $B$. The time taken to travel from $A$ to $B$ is 90 s and $A B = 1410 \mathrm {~m}$.
\begin{enumerate}[label=(\alph*)]
\item Sketch, in the space below, a speed-time graph to show the motion of the car from $A$ to $B$.
\item Calculate the deceleration of the car as it decelerates from $25 \mathrm {~m} \mathrm {~s} ^ { - 1 }$ to $10 \mathrm {~m} \mathrm {~s} ^ { - 1 }$.
Question 4 continued $\_\_\_\_$
\end{enumerate}
\hfill \mbox{\textit{Edexcel M1 2008 Q4 [9]}}