| Exam Board | OCR |
|---|---|
| Module | M1 (Mechanics 1) |
| Year | 2006 |
| Session | June |
| Marks | 11 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Constant acceleration (SUVAT) |
| Type | Displacement expressions and comparison |
| Difficulty | Moderate -0.8 This is a straightforward SUVAT/kinematics question requiring basic time calculations (distance/speed) for three segments, sketching a piecewise linear displacement-time graph, and finding an intersection point. All steps are routine applications of standard formulas with no conceptual challenges or problem-solving insight required. |
| Spec | 3.02b Kinematic graphs: displacement-time and velocity-time |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Mark | Guidance |
| Line segment \(AB\) of \(+\)ve slope from origin | B1 | SR: If straight line segments joined by curves, this B1 not awarded |
| Line segment \(BC\) of steeper \(+\)ve slope, shorter time interval than \(AB\) | B1 | |
| Line segment \(CD\) of less steep slope compared with \(BC\) | B1 | An \((x,t)\) graph is accepted with references to more/less steep reversed |
| Time intervals 80, 40, 40; \(t = 80, 120, 160\) | B1, B1 | May be implied; any 2 correct. Total: 6 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Mark | Guidance |
| Line joining \((0,0)\) and \((160, 360)\) | B1ft | 6 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Mark | Guidance |
| \(v = 360/160\) | M1 | Woman's velocity (\(= 2.25\)) |
| M1 | For equation of man's displacement in relevant interval | |
| \(s = 120 + 4.5(t - 80)\) | A1 | Accept omission of \(-80\) |
| \(2.25t\) | M1 | Woman's displacement, awarded even if \(t\) is interpreted differently in man's expression |
| \(t = 106\tfrac{2}{3}\) (107) | A1 | 5 Accept 106.6, 106.7 but not 106 |
| SR Construction method: plotting points on graph, \(t\) between 104 and 109 inclusive | M1, A1 | Candidates reading displacement intersection from graph, dividing by woman's speed to find \(t\); also get \(v = 360/160\) |
# Question 3:
## Part (i):
| Answer/Working | Mark | Guidance |
|---|---|---|
| Line segment $AB$ of $+$ve slope from origin | B1 | SR: If straight line segments joined by curves, this B1 not awarded |
| Line segment $BC$ of steeper $+$ve slope, shorter time interval than $AB$ | B1 | |
| Line segment $CD$ of less steep slope compared with $BC$ | B1 | An $(x,t)$ graph is accepted with references to more/less steep reversed |
| Time intervals 80, 40, 40; $t = 80, 120, 160$ | B1, B1 | May be implied; any 2 correct. **Total: 6** |
## Part (ii):
| Answer/Working | Mark | Guidance |
|---|---|---|
| Line joining $(0,0)$ and $(160, 360)$ | B1ft | **6** |
## Part (iii):
| Answer/Working | Mark | Guidance |
|---|---|---|
| $v = 360/160$ | M1 | Woman's velocity ($= 2.25$) |
| | M1 | For equation of man's displacement in relevant interval |
| $s = 120 + 4.5(t - 80)$ | A1 | Accept omission of $-80$ |
| $2.25t$ | M1 | Woman's displacement, awarded even if $t$ is interpreted differently in man's expression |
| $t = 106\tfrac{2}{3}$ (107) | A1 | **5** Accept 106.6, 106.7 but not 106 |
| SR Construction method: plotting points on graph, $t$ between 104 and 109 inclusive | M1, A1 | Candidates reading displacement intersection from graph, dividing by woman's speed to find $t$; also get $v = 360/160$ |
---3 A man travels 360 m along a straight road. He walks for the first 120 m at $1.5 \mathrm {~m} \mathrm {~s} ^ { - 1 }$, runs the next 180 m at $4.5 \mathrm {~m} \mathrm {~s} ^ { - 1 }$, and then walks the final 60 m at $1.5 \mathrm {~m} \mathrm {~s} ^ { - 1 }$. The man's displacement from his starting point after $t$ seconds is $x$ metres.\\
(i) Sketch the $( t , x )$ graph for the journey, showing the values of $t$ for which $x = 120,300$ and 360 .
A woman jogs the same 360 m route at constant speed, starting at the same instant as the man and finishing at the same instant as the man.\\
(ii) Draw a dotted line on your ( $t , x$ ) graph to represent the woman's journey.\\
(iii) Calculate the value of $t$ at which the man overtakes the woman.
\hfill \mbox{\textit{OCR M1 2006 Q3 [11]}}