| Exam Board | OCR |
|---|---|
| Module | M1 (Mechanics 1) |
| Marks | 17 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Travel graphs |
| Type | Distance from velocity function using calculus |
| Difficulty | Standard +0.3 This is a standard M1 kinematics question involving velocity-time graphs and basic calculus. Parts (i)-(ii) require finding area under a piecewise linear graph and calculating gradient (routine). Parts (iii)-(vi) involve straightforward differentiation and integration of a polynomial velocity function. All techniques are standard M1 content with no novel problem-solving required, though the multi-part structure and integration in part (vi) make it slightly above average difficulty. |
| Spec | 3.02b Kinematic graphs: displacement-time and velocity-time3.02c Interpret kinematic graphs: gradient and area3.02f Non-uniform acceleration: using differentiation and integration |
\includegraphics{figure_7}
A car $P$ starts from rest and travels along a straight road for $600$ s. The $(t, v)$ graph for the journey is shown in the diagram. This graph consists of three straight line segments. Find
\begin{enumerate}[label=(\roman*)]
\item the distance travelled by $P$, [3]
\item the deceleration of $P$ during the interval $500 < t < 600$. [2]
\end{enumerate}
Another car $Q$ starts from rest at the same instant as $P$ and travels in the same direction along the same road for $600$ s. At time $t$ s after starting the velocity of $Q$ is $(600t^2 - t^3) \times 10^{-6}$ m s$^{-1}$.
\begin{enumerate}[label=(\roman*)]
\setcounter{enumi}{2}
\item Find an expression in terms of $t$ for the acceleration of $Q$. [2]
\item Find how much less $Q$'s deceleration is than $P$'s when $t = 550$. [2]
\item Show that $Q$ has its maximum velocity when $t = 400$. [2]
\item Find how much further $Q$ has travelled than $P$ when $t = 400$. [6]
\end{enumerate}
\hfill \mbox{\textit{OCR M1 Q7 [17]}}