| Exam Board | Edexcel |
|---|---|
| Module | M1 (Mechanics 1) |
| Year | 2014 |
| Session | January |
| Marks | 17 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Constant acceleration (SUVAT) |
| Type | Sketch velocity-time graph |
| Difficulty | Moderate -0.3 This is a standard M1 SUVAT question with two particles moving in stages. Parts (a)-(c) involve routine sketching, applying v=u+at, and solving linear equations. Part (d) requires calculating areas under speed-time graphs. While multi-part with several steps, it follows predictable M1 patterns 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 formulae3.02e Two-dimensional constant acceleration: with vectors |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Guidance |
| Isosceles trapezium from origin finishing on \(t\)-axis | B1 | First B1 for isosceles (approx.) trapezium, from origin, finishing on the \(t\)-axis |
| Isosceles triangle from origin finishing on \(t\)-axis at same point, overlapping twice | B1 | Second B1 for isosceles (approx.) triangle, from origin, finishing on \(t\)-axis at same point *and* overlapping twice |
| Values \(30, 90, 150, 180\) placed correctly | B1 (3) | Allow delineators |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Guidance |
| \(\frac{1}{2}(90+60)\cdot 20 = 1500\) | M1 A1 | First M1 for complete method to find distance (or half distance) between stations; A1 for correct expression |
| \(1500 = \frac{1}{2}a\cdot 90^2\) | M1 A1 ft | Second M1 for complete method to find \(a\) (M0 if \(s\) = full distance used in any suvat equation); A1 ft on their distance |
| \(a = \frac{10}{27}\ \text{ms}^{-2}\) or decimal | A1 (5) | Third A1 for \(10/27\) oe, \(0.37\) or better |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Guidance |
| \(\frac{10t}{27} = 20\) | M1 A1 | First M1 for (their \(a\)) \(\times t = 20\) (or their \(v\) max for \(A\)); A1 for correct equation |
| \(t = 54\ \text{s}\) | A1 | Second A1 for \(54\) (\(t_1\)) (\(54.1\) A0) |
| \(t = 126\ \text{s}\) | A1 ft (4) | Third A1 ft for \((180-t_1)\), provided \(30 < t_1 < 90\) |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Guidance |
| \(\frac{10}{27}\times 90\left(=\frac{100}{3}\right)\) | M1 | First M1 for finding max speed of \(B\), e.g. their \(a\times 90\); must be seen in (d) |
| \(\frac{100}{3}\times 6 - \frac{1}{2}\cdot\frac{10}{27}\cdot 6^2\left(=\frac{580}{3}\right)\) | DM1 A1 | Second M1 for complete method to find distance moved by \(B\) between \(t=90\) and \(t=96\); A1 for correct expression |
| \(d = \frac{580}{3}-(20\times 6)\) | DM1 | Third DM1 dependent on first and second M marks, for complete method to find required distance |
| \(= \frac{220}{3}\ \text{m}\) or decimal | A1 (5) | Second A1 for \(220/3\) m oe, \(73\) m or better |
## Question 8:
### Part (a):
| Answer/Working | Marks | Guidance |
|---|---|---|
| Isosceles trapezium from origin finishing on $t$-axis | B1 | First B1 for isosceles (approx.) trapezium, from origin, finishing on the $t$-axis |
| Isosceles triangle from origin finishing on $t$-axis at same point, overlapping twice | B1 | Second B1 for isosceles (approx.) triangle, from origin, finishing on $t$-axis at same point *and* overlapping twice |
| Values $30, 90, 150, 180$ placed correctly | B1 (3) | Allow delineators |
### Part (b):
| Answer/Working | Marks | Guidance |
|---|---|---|
| $\frac{1}{2}(90+60)\cdot 20 = 1500$ | M1 A1 | First M1 for complete method to find distance (or half distance) between stations; A1 for correct expression |
| $1500 = \frac{1}{2}a\cdot 90^2$ | M1 A1 ft | Second M1 for complete method to find $a$ (M0 if $s$ = full distance used in any suvat equation); A1 ft on their distance |
| $a = \frac{10}{27}\ \text{ms}^{-2}$ or decimal | A1 (5) | Third A1 for $10/27$ oe, $0.37$ or better |
### Part (c):
| Answer/Working | Marks | Guidance |
|---|---|---|
| $\frac{10t}{27} = 20$ | M1 A1 | First M1 for (their $a$) $\times t = 20$ (or their $v$ max for $A$); A1 for correct equation |
| $t = 54\ \text{s}$ | A1 | Second A1 for $54$ ($t_1$) ($54.1$ A0) |
| $t = 126\ \text{s}$ | A1 ft (4) | Third A1 ft for $(180-t_1)$, provided $30 < t_1 < 90$ |
### Part (d):
| Answer/Working | Marks | Guidance |
|---|---|---|
| $\frac{10}{27}\times 90\left(=\frac{100}{3}\right)$ | M1 | First M1 for finding max speed of $B$, e.g. their $a\times 90$; must be seen in (d) |
| $\frac{100}{3}\times 6 - \frac{1}{2}\cdot\frac{10}{27}\cdot 6^2\left(=\frac{580}{3}\right)$ | DM1 A1 | Second M1 for complete method to find distance moved by $B$ between $t=90$ and $t=96$; A1 for correct expression |
| $d = \frac{580}{3}-(20\times 6)$ | DM1 | Third DM1 dependent on first and second M marks, for complete method to find required distance |
| $= \frac{220}{3}\ \text{m}$ or decimal | A1 (5) | Second A1 for $220/3$ m oe, $73$ m or better |8. Two trains, $A$ and $B$, start together from rest, at time $t = 0$, at a station and move along parallel straight horizontal tracks. Both trains come to rest at the next station after 180 s . Train $A$ moves with constant acceleration $\frac { 2 } { 3 } \mathrm {~m} \mathrm {~s} ^ { - 2 }$ for 30 s , then moves at constant speed for 120 s and then moves with constant deceleration for the final 30 s . Train $B$ moves with constant acceleration for 90 s and then moves with constant deceleration for the final 90 s .
\begin{enumerate}[label=(\alph*)]
\item Sketch, on the same axes, the speed-time graphs for the motion of the two trains between the two stations.
\item Find the acceleration of train $B$ for the first half of its journey.
\item Find the times when the two trains are moving at the same speed.
\item Find the distance between the trains 96 s after they start.\\
\includegraphics[max width=\textwidth, alt={}, center]{fade35da-8dca-4d98-a07c-ed3a173fccda-28_43_58_2457_1893}
\end{enumerate}
\hfill \mbox{\textit{Edexcel M1 2014 Q8 [17]}}