CAIE M1 2010 June — Question 2 5 marks

Exam BoardCAIE
ModuleM1 (Mechanics 1)
Year2010
SessionJune
Marks5
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicVariable acceleration (1D)
TypeDisplacement from velocity by integration
DifficultyModerate -0.3 This is a straightforward mechanics question requiring differentiation to find acceleration, solving a linear equation for time, then integration to find displacement. All steps are routine applications of standard techniques with no conceptual challenges, making it slightly easier than average.
Spec1.08a Fundamental theorem of calculus: integration as reverse of differentiation3.02f Non-uniform acceleration: using differentiation and integration

2 A particle starts at a point \(O\) and moves along a straight line. Its velocity \(t\) s after leaving \(O\) is \(\left( 1.2 t - 0.12 t ^ { 2 } \right) \mathrm { m } \mathrm { s } ^ { - 1 }\). Find the displacement of the particle from \(O\) when its acceleration is \(0.6 \mathrm {~m} \mathrm {~s} ^ { - 2 }\).

Question 2:
AnswerMarks Guidance
Answer/WorkingMarks Guidance
\(1.2 - 0.24t = 0.6\)M1 For using \(a = dv/dt\) and attempting to solve \(a = 0.6\)
\(t = 2.5\)A1
\(s = 0.6t^2 - 0.04t^3\)M1 For using \(s = \int v\,dt\)
\(s = (0.6 \times 2.5^2 - 0.04 \times 2.5^3) - (0-0)\)DM1 For using limits 0 to 2.5 or equivalent (dependent on integration)
Displacement is 3.125 mA1 Accept 3.12 or 3.13
[5]
## Question 2:

| Answer/Working | Marks | Guidance |
|---|---|---|
| $1.2 - 0.24t = 0.6$ | M1 | For using $a = dv/dt$ and attempting to solve $a = 0.6$ |
| $t = 2.5$ | A1 | |
| $s = 0.6t^2 - 0.04t^3$ | M1 | For using $s = \int v\,dt$ |
| $s = (0.6 \times 2.5^2 - 0.04 \times 2.5^3) - (0-0)$ | DM1 | For using limits 0 to 2.5 or equivalent (dependent on integration) |
| Displacement is 3.125 m | A1 | Accept 3.12 or 3.13 |
| **[5]** | | |

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2 A particle starts at a point $O$ and moves along a straight line. Its velocity $t$ s after leaving $O$ is $\left( 1.2 t - 0.12 t ^ { 2 } \right) \mathrm { m } \mathrm { s } ^ { - 1 }$. Find the displacement of the particle from $O$ when its acceleration is $0.6 \mathrm {~m} \mathrm {~s} ^ { - 2 }$.

\hfill \mbox{\textit{CAIE M1 2010 Q2 [5]}}