WJEC Unit 2 Specimen — Question 8 5 marks

Exam BoardWJEC
ModuleUnit 2 (Unit 2)
SessionSpecimen
Marks5
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicVariable acceleration (1D)
TypeDisplacement from velocity by integration
DifficultyModerate -0.8 This is a straightforward mechanics question requiring basic calculus operations: integrating velocity to find displacement (with initial condition) and differentiating velocity to find acceleration. Both are standard A-level techniques with no problem-solving insight required, making it easier than average but not trivial due to the multi-step nature and need to apply the initial condition correctly.
Spec3.02a Kinematics language: position, displacement, velocity, acceleration3.02f Non-uniform acceleration: using differentiation and integration

A particle \(P\), of mass 3 kg, moves along the horizontal \(x\)-axis under the action of a resultant force \(F\) N. Its velocity \(v\) ms\(^{-1}\) at time \(t\) seconds is given by $$v = 12t - 3t^2.$$
  1. Given that the particle is at the origin \(O\) when \(t = 1\), find an expression for the displacement of the particle from \(O\) at time \(t\) s. [3]
  2. Find an expression for the acceleration of the particle at time \(t\) s. [2]

A particle $P$, of mass 3 kg, moves along the horizontal $x$-axis under the action of a resultant force $F$ N. Its velocity $v$ ms$^{-1}$ at time $t$ seconds is given by

$$v = 12t - 3t^2.$$

\begin{enumerate}[label=(\alph*)]
\item Given that the particle is at the origin $O$ when $t = 1$, find an expression for the displacement of the particle from $O$ at time $t$ s. [3]

\item Find an expression for the acceleration of the particle at time $t$ s. [2]
\end{enumerate}

\hfill \mbox{\textit{WJEC Unit 2  Q8 [5]}}