| Exam Board | CAIE |
|---|---|
| Module | M1 (Mechanics 1) |
| Year | 2020 |
| Session | November |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Variable acceleration (1D) |
| Type | Variable acceleration with initial conditions |
| Difficulty | Moderate -0.3 This is a straightforward integration problem requiring standard application of calculus to kinematics. Students integrate a=0.1t^(3/2) to find velocity (using initial condition v=1.72), solve for t when v=3, then integrate again for displacement. While it involves fractional powers, the technique is routine for M1 level with no conceptual challenges or problem-solving insight required—slightly easier than average due to its mechanical nature. |
| Spec | 1.08d Evaluate definite integrals: between limits3.02f Non-uniform acceleration: using differentiation and integration |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Mark | Guidance |
| \(\int 0.1t^{3/2}\,dt\) | *M1 | For integrating \(a\) |
| \(v = 0.04t^{5/2} + 1.72\) | A1 | |
| \(0.04t^{5/2} + 1.72 = 3\) | DM1 | For attempting to solve the equation \(v = 3\), to obtain \(t\) |
| \(t = 4\) | A1 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Mark | Guidance |
| \(\int\!\left(0.04t^{5/2} + 1.72\right)dt\), \(\left[s = \frac{2}{175}t^{7/2} + 1.72t\,(+C')\right]\) | *M1 | For integrating \(v\) which itself has come from integration |
| For using correct limits correctly | DM1 | |
| Displacement when \(t = 2\) is \(3.57\) m | A1 |
## Question 7(a):
| Answer | Mark | Guidance |
|--------|------|----------|
| $\int 0.1t^{3/2}\,dt$ | *M1 | For integrating $a$ |
| $v = 0.04t^{5/2} + 1.72$ | A1 | |
| $0.04t^{5/2} + 1.72 = 3$ | DM1 | For attempting to solve the equation $v = 3$, to obtain $t$ |
| $t = 4$ | A1 | |
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## Question 7(b):
| Answer | Mark | Guidance |
|--------|------|----------|
| $\int\!\left(0.04t^{5/2} + 1.72\right)dt$, $\left[s = \frac{2}{175}t^{7/2} + 1.72t\,(+C')\right]$ | *M1 | For integrating $v$ which itself has come from integration |
| For using correct limits correctly | DM1 | |
| Displacement when $t = 2$ is $3.57$ m | A1 | |
---7 A particle $P$ moves in a straight line, starting from a point $O$ with velocity $1.72 \mathrm {~m} \mathrm {~s} ^ { - 1 }$. The acceleration $a \mathrm {~m} \mathrm {~s} ^ { - 2 }$ of the particle, $t \mathrm {~s}$ after leaving $O$, is given by $a = 0.1 t ^ { \frac { 3 } { 2 } }$.
\begin{enumerate}[label=(\alph*)]
\item Find the value of $t$ when the velocity of $P$ is $3 \mathrm {~m} \mathrm {~s} ^ { - 1 }$.
\item Find the displacement of $P$ from $O$ when $t = 2$, giving your answer correct to 2 decimal places. [3]
\end{enumerate}
\hfill \mbox{\textit{CAIE M1 2020 Q7 [7]}}