| Exam Board | Edexcel |
|---|---|
| Module | M3 (Mechanics 3) |
| Year | 2001 |
| Session | June |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Variable acceleration (1D) |
| Type | Velocity from acceleration by integration |
| Difficulty | Moderate -0.3 This is a straightforward variable acceleration question requiring integration of a simple exponential function with an initial condition, followed by substitution and finding a limit. While it's M3 (Further Maths), the mathematical techniques are routine: integrate e^(-2t), apply boundary condition, substitute t=3, and recognize the limit as tââ. No problem-solving insight needed, just methodical application of standard calculus. |
| Spec | 6.06a Variable force: dv/dt or v*dv/dx methods |
A particle $P$ moves along the x-axis in the positive direction. At time $t$ seconds, the velocity of $P$ is $v$ m s$^{-1}$ and its acceleration is $\frac{1}{5}e^{-2t}$ m s$^{-2}$. When $t = 0$ the speed of $P$ is 10 m s$^{-1}$.
\begin{enumerate}[label=(\alph*)]
\item Express $v$ in terms of $t$. [4]
\item Find, to 3 significant figures, the speed of $P$ when $t = 3$. [2]
\item Find the limiting value of $v$. [1]
\end{enumerate}
\hfill \mbox{\textit{Edexcel M3 2001 Q1 [7]}}