| Exam Board | Edexcel |
|---|---|
| Module | M1 (Mechanics 1) |
| Year | 2005 |
| Session | June |
| Marks | 10 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Travel graphs |
| Type | Multi-stage motion with all parameters given |
| Difficulty | Moderate -0.8 This is a straightforward kinematics problem using constant acceleration equations and speed-time graphs. Part (a) requires sketching a standard three-phase motion graph, part (b) uses the trapezium area formula or SUVAT equations directly, and part (c) involves finding the final deceleration phase duration using known total distance. All techniques are routine M1 material with clear signposting and no problem-solving insight required. |
| Spec | 3.02a Kinematics language: position, displacement, velocity, acceleration3.02b Kinematic graphs: displacement-time and velocity-time3.02c Interpret kinematic graphs: gradient and area3.02d Constant acceleration: SUVAT formulae |
| Answer | Marks |
|---|---|
| 5 | (a) 10 Shape 0 < t < 12 |
| Answer | Marks |
|---|---|
| Hence total time = 27 + 8 = 35 s | B1 |
Question 5:
5 | (a) 10 Shape 0 < t < 12
Shape t > 12
3
Figures
12 27
(b) Distance in 1st 12 s = ½ x (10 + 3) x 12 or (3 x 12) + ½ x 3 x 7
= 78 m
(c) either
distance from t = 12 to t = 27 = 15 x 3 = 45
∴ distance in last section = 135 – 45 = 12 m
½ x 3 x t = 12,
⇒ t = 8 s
hence total time = 27 + 8 = 35 s
or Distance remaining after 12 s = 135 – 78 = 57 m
½ x (15 + 15 + t) x 3 = 57
⇒ t = 8
Hence total time = 27 + 8 = 35 s | B1
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A1A train is travelling at $10 \text{ m s}^{-1}$ on a straight horizontal track. The driver sees a red signal 135 m ahead and immediately applies the brakes. The train immediately decelerates with constant deceleration for 12 s, reducing its speed to $3 \text{ m s}^{-1}$. The driver then releases the brakes and allows the train to travel at a constant speed of $3 \text{ m s}^{-1}$ for a further 15 s. He then applies the brakes again and the train slows down with constant deceleration, coming to rest as it reaches the signal.
\begin{enumerate}[label=(\alph*)]
\item Sketch a speed-time graph to show the motion of the train, [3]
\item Find the distance travelled by the train from the moment when the brakes are first applied to the moment when its speed first reaches $3 \text{ m s}^{-1}$. [2]
\item Find the total time from the moment when the brakes are first applied to the moment when the train comes to rest. [5]
\end{enumerate}
\hfill \mbox{\textit{Edexcel M1 2005 Q5 [10]}}