| Exam Board | Pre-U |
|---|---|
| Module | Pre-U 9794/3 (Pre-U Mathematics Paper 3) |
| Year | 2020 |
| Session | Specimen |
| Marks | 6 |
| Topic | Variable acceleration (1D) |
| Type | Finding when particle at rest |
| Difficulty | Moderate -0.3 This is a straightforward mechanics question requiring basic calculus skills. Part (a) involves factorising a cubic (which factors nicely) and solving v=0. Part (b) requires integrating the velocity function to find displacement. Both parts are standard textbook exercises with no problem-solving insight needed, making it slightly easier than average but not trivial due to the cubic manipulation and integration steps required. |
| Spec | 1.08d Evaluate definite integrals: between limits3.02a Kinematics language: position, displacement, velocity, acceleration |
A particle travels along a straight line. Its velocity $v$ ms$^{-1}$ after $t$ seconds is given by
$$v = t^3 - 9t^2 + 20t$$
When $t = 0$, the particle is at rest at $P$.
\begin{enumerate}[label=(\alph*)]
\item Find the times, other than $t = 0$, at which the particle is at rest. [2]
\item Find the displacement of the particle from $P$ when $t = 2$. [4]
\end{enumerate}
\hfill \mbox{\textit{Pre-U Pre-U 9794/3 2020 Q7 [6]}}