| Exam Board | OCR |
|---|---|
| Module | M1 (Mechanics 1) |
| Marks | 12 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Travel graphs |
| Type | Distance from velocity function using calculus |
| Difficulty | Moderate -0.3 This is a standard M1 kinematics question requiring integration of acceleration to find velocity and displacement. While it involves piecewise functions and multiple steps (12 marks total), the techniques are routine: integrate a=1.8t, apply initial conditions, then use constant acceleration formulas. No novel problem-solving or geometric insight required—slightly easier than average due to straightforward application of standard methods. |
| Spec | 3.02d Constant acceleration: SUVAT formulae3.02f Non-uniform acceleration: using differentiation and integration |
A particle starts from rest at a point $A$ at time $t = 0$, where $t$ is in seconds. The particle moves in a straight line. For $0 \leq t \leq 4$ the acceleration is $1.8t$ m s$^{-2}$, and for $4 \leq t \leq 7$ the particle has constant acceleration $7.2$ m s$^{-2}$.
\begin{enumerate}[label=(\roman*)]
\item Find an expression for the velocity of the particle in terms of $t$, valid for $0 \leq t \leq 4$. [3]
\item Show that the displacement of the particle from $A$ is $19.2$ m when $t = 4$. [4]
\item Find the displacement of the particle from $A$ when $t = 7$. [5]
\end{enumerate}
\hfill \mbox{\textit{OCR M1 Q5 [12]}}