| Exam Board | Edexcel |
|---|---|
| Module | M1 (Mechanics 1) |
| Year | 2003 |
| Session | November |
| Marks | 12 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Travel graphs |
| Type | Multi-stage motion with algebraic unknowns |
| Difficulty | Moderate -0.3 This is a standard M1 kinematics question involving speed-time graphs and constant acceleration equations. Part (a) is routine sketching, part (b) uses area under graph equals distance, and parts (c)-(d) apply SUVAT equations with careful attention to timing. While multi-step, all techniques are textbook standard with no novel problem-solving required, making it slightly easier than average. |
| Spec | 3.02b Kinematic graphs: displacement-time and velocity-time3.02c Interpret kinematic graphs: gradient and area3.02d Constant acceleration: SUVAT formulae |
| Answer | Marks | Guidance |
|---|---|---|
| Shape | B1 | (2) |
| Figs | B1 |
| Answer | Marks | Guidance |
|---|---|---|
| \(\frac{1}{2}(T + 120) \times 25 = 4000\) | M1 | A1 |
| or \(\left[\frac{1}{2} \cdot 20 \cdot 25 + 120 \cdot 25 + \frac{1}{2}(T - 140) \cdot 25 = 4000\right]\) | A1 | |
| \(\rightarrow T = 200\) s | (3) |
| Answer | Marks | Guidance |
|---|---|---|
| Car: \(\frac{1}{2} \cdot 20 \cdot 25 + 25(t - 20) = 1500\) | M1 | A1, A1 |
| \(\rightarrow t = 70\) s | M1 | A1 |
| Hence motorcycle travels for 60 s | (5) |
| Answer | Marks | Guidance |
|---|---|---|
| \(1500 = \left(\frac{0 + v}{2}\right) \cdot 60\) | M1 | |
| \(v = 50 \text{ m s}^{-1}\) | A1 |
## (a)
Shape | B1 | (2)
Figs | B1 |
## (b)
$\frac{1}{2}(T + 120) \times 25 = 4000$ | M1 | A1
or $\left[\frac{1}{2} \cdot 20 \cdot 25 + 120 \cdot 25 + \frac{1}{2}(T - 140) \cdot 25 = 4000\right]$ | | A1
$\rightarrow T = 200$ s | | (3)
## (c)
Car: $\frac{1}{2} \cdot 20 \cdot 25 + 25(t - 20) = 1500$ | M1 | A1, A1
$\rightarrow t = 70$ s | M1 | A1
Hence motorcycle travels for 60 s | | (5)
## (d)
$1500 = \left(\frac{0 + v}{2}\right) \cdot 60$ | M1 |
$v = 50 \text{ m s}^{-1}$ | | A1
**Total: 12 marks**
---A car starts from rest at a point $S$ on a straight racetrack. The car moves with constant acceleration for 20 s, reaching a speed of 25 m s$^{-1}$. The car then travels at a constant speed of 25 m s$^{-1}$ for 120 s. Finally it moves with constant deceleration, coming to rest at a point $F$.
\begin{enumerate}[label=(\alph*)]
\item In the space below, sketch a speed-time graph to illustrate the motion of the car. [2]
\end{enumerate}
The distance between $S$ and $F$ is 4 km.
\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{1}
\item Calculate the total time the car takes to travel from $S$ to $F$. [3]
\end{enumerate}
A motorcycle starts at $S$, 10 s after the car has left $S$. The motorcycle moves with constant acceleration from rest and passes the car at a point $P$ which is 1.5 km from $S$. When the motorcycle passes the car, the motorcycle is still accelerating and the car is moving at a constant speed. Calculate
\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{2}
\item the time the motorcycle takes to travel from $S$ to $P$, [5]
\item the speed of the motorcycle at $P$. [2]
\end{enumerate}
\hfill \mbox{\textit{Edexcel M1 2003 Q4 [12]}}