| Exam Board | OCR |
|---|---|
| Module | FM1 AS (Further Mechanics 1 AS) |
| Year | 2021 |
| Session | June |
| Marks | 8 |
| Topic | Dimensional Analysis |
| Type | Find exponents with partial constraints |
| Difficulty | Standard +0.3 This is a straightforward dimensional analysis problem requiring students to equate dimensions on both sides and solve simultaneous equations, followed by a simple special case check. While it involves multiple variables, the method is standard and taught explicitly in FM1, making it slightly easier than average A-level difficulty. |
| Spec | 6.01a Dimensions: M, L, T notation6.01d Unknown indices: using dimensions |
2 A particle moves in a straight line with constant acceleration. Its initial and final velocities are $u$ and $v$ respectively and at time $t$ its displacement from its starting position is $s$. An equation connecting these quantities is $s = k \left( u ^ { \alpha } + v ^ { \beta } \right) t ^ { \gamma }$, where $k$ is a dimensionless constant.
\begin{enumerate}[label=(\alph*)]
\item Use dimensional analysis to find the values of $\alpha , \beta$ and $\gamma$.
\item By considering the case where the acceleration is zero, determine the value of $k$.
\end{enumerate}
\hfill \mbox{\textit{OCR FM1 AS 2021 Q2 [8]}}