| Exam Board | WJEC |
|---|---|
| Module | Unit 4 (Unit 4) |
| Year | 2019 |
| Session | June |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Variable Force |
| Type | Air resistance kv - horizontal motion |
| Difficulty | Standard +0.3 This is a standard mechanics differential equation question requiring Newton's second law (F=ma), separation of variables, and partial fractions. The steps are routine for A-level mechanics: set up the equation, separate variables, integrate using standard techniques, and apply initial conditions. The critical comment requires recognizing that v²-resistance implies the box never stops, which is physically unrealistic. While it involves calculus and mechanics together, all techniques are standard bookwork with no novel insight required, making it slightly easier than average. |
| Spec | 6.06a Variable force: dv/dt or v*dv/dx methods |
A box of mass $2$ kg is projected along a horizontal surface with an initial velocity of $5$ ms$^{-1}$. The box experiences a variable resistive force of $0.4v^2$ N, where $v$ ms$^{-1}$ is the velocity of the box at time $t$ seconds.
\begin{enumerate}[label=(\alph*)]
\item Show that $v$ satisfies the equation
$$5\frac{dv}{dt} + v^2 = 0.$$ [2]
\item Find an expression for $v$ in terms of $t$. [4]
\item Briefly explain why this model is not particularly realistic. [1]
\end{enumerate}
\hfill \mbox{\textit{WJEC Unit 4 2019 Q8 [7]}}