| Exam Board | SPS |
|---|---|
| Module | SPS SM Mechanics (SPS SM Mechanics) |
| Year | 2021 |
| Session | September |
| Marks | 13 |
| Topic | Variable acceleration (1D) |
| Type | Collision or meeting problems |
| Difficulty | Moderate -0.3 This is a straightforward kinematics problem requiring substitution into a given position function, differentiation to find velocity and acceleration, and solving a quadratic equation for when two objects meet. All techniques are standard A-level mechanics with no novel problem-solving required, though part (c) involves careful setup of equations and algebraic manipulation, making it slightly easier than average overall. |
| Spec | 1.07b Gradient as rate of change: dy/dx notation1.07i Differentiate x^n: for rational n and sums3.02f Non-uniform acceleration: using differentiation and integration |
A car starts from the point $A$. At time $t$ s after leaving $A$, the distance of the car from $A$ is $s$ m, where $s = 30t - 0.4t^2$, $0 \leq t \leq 25$. The car reaches the point $B$ when $t = 25$.
\begin{enumerate}[label=(\alph*)]
\item Find the distance $AB$. [2]
\item Show that the car travels with a constant acceleration and state the value of this acceleration. [3]
\end{enumerate}
A runner passes through $B$ when $t = 0$ with an initial velocity of $2 \text{ m s}^{-1}$ running directly towards $A$. The runner has a constant acceleration of $0.1 \text{ m s}^{-2}$.
\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{2}
\item Find the distance from $A$ at which the runner and the car pass one another. [8]
\end{enumerate}
\hfill \mbox{\textit{SPS SPS SM Mechanics 2021 Q4 [13]}}