| Exam Board | Pre-U |
|---|---|
| Module | Pre-U 9794/3 (Pre-U Mathematics Paper 3) |
| Year | 2014 |
| Session | June |
| Marks | 10 |
| Topic | Variable acceleration (1D) |
| Type | Variable acceleration with initial conditions |
| Difficulty | Moderate -0.3 This is a straightforward kinematics question requiring integration of acceleration to find velocity and displacement, with standard initial conditions. While it involves multiple steps and interpreting when the particle returns to O (requiring solving a quadratic), these are routine A-level mechanics techniques with no novel problem-solving required. Slightly easier than average due to the simple polynomial form and clear structure. |
| Spec | 3.02d Constant acceleration: SUVAT formulae3.02f Non-uniform acceleration: using differentiation and integration |
A particle $P$ is free to move along a straight line $Ox$. It starts from rest at $O$ and after $t$ seconds its acceleration $a \mathrm{~m} \mathrm{~s}^{-2}$ is given by $a = 12 - 6t$.
\begin{enumerate}[label=(\roman*)]
\item Find an expression in terms of $t$ for its velocity $v \mathrm{~m} \mathrm{~s}^{-1}$. Hence find the velocity of $P$ when $t = 4$. [4]
\item Find the displacement of $P$ from $O$ when $t = 4$. [3]
\item Find the velocity of $P$ when it returns to $O$. [3]
\end{enumerate}
\hfill \mbox{\textit{Pre-U Pre-U 9794/3 2014 Q10 [10]}}