| Exam Board | CAIE |
|---|---|
| Module | M1 (Mechanics 1) |
| Year | 2014 |
| Session | June |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Travel graphs |
| Type | Velocity from displacement function using calculus |
| Difficulty | Moderate -0.8 This is a straightforward kinematics question requiring only standard differentiation of a polynomial (once for velocity, twice for acceleration) and solving a simple quadratic equation. These are routine A-level techniques with no problem-solving insight needed, making it easier than average but not trivial since it requires correct application of calculus in a mechanics context. |
| Spec | 1.07i Differentiate x^n: for rational n and sums3.02a Kinematics language: position, displacement, velocity, acceleration |
| Answer | Marks |
|---|---|
| 1 | DF = 28000 |
| Answer | Marks |
|---|---|
| V = 47.5 | B1 |
| Answer | Marks | Guidance |
|---|---|---|
| A1 | [3] | For using P = (DF)V |
Question 1:
1 | DF = 28000
[1330 000 = 28000V]
V = 47.5 | B1
M1
A1 | [3] | For using P = (DF)VA particle moves in a straight line. At time $t$ seconds, its displacement from a fixed point is $s$ metres, where
$$s = t^3 - 6t^2 + 9t$$
\begin{enumerate}[label=(\alph*)]
\item Find expressions for the velocity and acceleration of the particle at time $t$. [4]
\item Find the times when the particle is at rest. [2]
\end{enumerate}
\hfill \mbox{\textit{CAIE M1 2014 Q1 [6]}}