| Exam Board | Edexcel |
|---|---|
| Module | M1 (Mechanics 1) |
| Year | 2017 |
| Session | June |
| Marks | 13 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Constant acceleration (SUVAT) |
| Type | Sketch velocity-time graph |
| Difficulty | Standard +0.3 This is a standard M1 two-particle kinematics problem requiring sketching speed-time graphs, finding when speeds are equal (simple algebra), and using areas under graphs to find when Q overtakes P. All techniques are routine for M1 students with no novel insight 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 |
|---|---|---|
| Answer/Working | Mark | Guidance |
| One graph correct shape | B1 | |
| Both graphs correct shape, on same sketch and intersecting (with different start times) | B1 | Figs 10, 20, 25, 40 shown (with 20 as the second start time) |
| Correct figures shown | B1 | Ignore all vertical lines |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Mark | Guidance |
| \(20 + 10\) | M1 | Complete method |
| \(= 30\) | A1 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Mark | Guidance |
| \(\dfrac{40}{t_1 - 20} = \dfrac{25}{10}\) | M1 | Complete method to find time when \(Q\) reaches \(40\text{ m s}^{-1}\) |
| Correct unsimplified equation | A1 | |
| \(\Rightarrow t_1 = 36\) | A1 | |
| Time to reach \(40\text{ m s}^{-1}\) is \(\dfrac{40}{2.5}(=16)\) (M1A1) | ||
| Time from start \(= \dfrac{40}{2.5} + 20 = 36\) (A1) | (seen or implied) | |
| \(\dfrac{(T+T-10)}{2}\times25\) | M1 | Find distance travelled by either train at \(t=T\) |
| One correct | A1 | |
| \(\dfrac{(T-20+T-36)}{2}\times40\) | A1ft | Both correct. Follow their 36 |
| Equate and solve for \(T\) | dM1 | |
| \(T = 66\tfrac{1}{3}\) | A1 | Accept 66 or better |
## Question 5(a):
| Answer/Working | Mark | Guidance |
|---|---|---|
| One graph correct shape | B1 | |
| Both graphs correct shape, on same sketch and intersecting (with different start times) | B1 | Figs 10, 20, 25, 40 shown (with 20 as the second start time) |
| Correct figures shown | B1 | Ignore all vertical lines |
## Question 5(b):
| Answer/Working | Mark | Guidance |
|---|---|---|
| $20 + 10$ | M1 | Complete method |
| $= 30$ | A1 | |
## Question 5(c):
| Answer/Working | Mark | Guidance |
|---|---|---|
| $\dfrac{40}{t_1 - 20} = \dfrac{25}{10}$ | M1 | Complete method to find time when $Q$ reaches $40\text{ m s}^{-1}$ |
| Correct unsimplified equation | A1 | |
| $\Rightarrow t_1 = 36$ | A1 | |
| Time to reach $40\text{ m s}^{-1}$ is $\dfrac{40}{2.5}(=16)$ (M1A1) | | |
| Time from start $= \dfrac{40}{2.5} + 20 = 36$ (A1) | | (seen or implied) |
| $\dfrac{(T+T-10)}{2}\times25$ | M1 | Find distance travelled by either train at $t=T$ |
| One correct | A1 | |
| $\dfrac{(T-20+T-36)}{2}\times40$ | A1ft | Both correct. Follow their 36 |
| Equate and solve for $T$ | dM1 | |
| $T = 66\tfrac{1}{3}$ | A1 | Accept 66 or better |\begin{enumerate}
\item Two trains, $P$ and $Q$, move on horizontal parallel straight tracks. Initially both are at rest in a station and level with each other. At time $t = 0 , P$ starts off and moves with constant acceleration for 10 s up to a speed of $25 \mathrm {~m} \mathrm {~s} ^ { - 1 }$ and then moves at a constant speed of $25 \mathrm {~m} \mathrm {~s} ^ { - 1 }$. At time $t = 20$, where $t$ is measured in seconds, train $Q$ starts to move in the same direction as $P$. Train $Q$ accelerates with the same initial constant acceleration as $P$, up to a speed of $40 \mathrm {~m} \mathrm {~s} ^ { - 1 }$ and then moves at a constant speed of $40 \mathrm {~m} \mathrm {~s} ^ { - 1 }$. Train $Q$ overtakes $P$ at time $t = T$, after both trains have reached their constant speeds.\\
(a) Sketch, on the same axes, the speed-time graphs of both trains for $0 \leqslant t \leqslant T$.\\
(b) Find the value of $t$ at the instant when both trains are moving at the same speed.\\
(c) Find the value of $T$.
\end{enumerate}
\hfill \mbox{\textit{Edexcel M1 2017 Q5 [13]}}