| Exam Board | SPS |
|---|---|
| Module | SPS FM Mechanics (SPS FM Mechanics) |
| Year | 2021 |
| Session | September |
| Marks | 7 |
| Topic | Constant acceleration (SUVAT) |
| Type | Sketch velocity-time graph |
| Difficulty | Moderate -0.8 This is a straightforward kinematics problem requiring a velocity-time graph sketch and distance calculation using trapezium areas. The multi-phase motion adds slight complexity, but the constant accelerations and clear structure make it routine for Further Maths students. All values are given explicitly, requiring only systematic application of distance = area under v-t graph. |
| Spec | 3.02b Kinematic graphs: displacement-time and velocity-time3.02c Interpret kinematic graphs: gradient and area3.02d Constant acceleration: SUVAT formulae |
A car is initially travelling with a constant velocity of $15 \text{ m s}^{-1}$ for $T$ s. It then decelerates at a constant rate for $\frac{T}{2}$ s, reaching a velocity of $10 \text{ m s}^{-1}$. It then immediately accelerates at a constant rate for $\frac{3T}{2}$ s reaching a velocity of $20 \text{ m s}^{-1}$.
\begin{enumerate}[label=(\alph*)]
\item Sketch a velocity–time graph to illustrate the motion. [3]
\item Given that the car travels a total distance of 1312.5 m over the journey described, find the value of $T$. [4]
\end{enumerate}
\hfill \mbox{\textit{SPS SPS FM Mechanics 2021 Q1 [7]}}