Challenging +1.2 This is a straightforward application of Euler's method with clearly stated forces and initial conditions. While it requires setting up Newton's second law (F=ma), differentiating to get dv/dt, and performing iterative calculations, the method is entirely procedural with no conceptual challenges. The 6 marks reflect computational work rather than problem-solving insight. Slightly above average difficulty due to being Further Maths and requiring careful arithmetic over multiple steps.
A particle of mass 4 kg moves horizontally in a straight line.
At time \(t\) seconds the velocity of the particle is \(v\) m s\(^{-1}\)
The following horizontal forces act on the particle:
β’ a constant driving force of magnitude 1.8 newtons
β’ another driving force of magnitude \(30\sqrt{t}\) newtons
β’ a resistive force of magnitude \(0.08v^2\) newtons
When \(t = 70\), \(v = 54\)
Use Euler's method with a step length of 0.5 to estimate the velocity of the particle after 71 seconds.
Give your answer to four significant figures.
[6 marks]
A particle of mass 4 kg moves horizontally in a straight line.
At time $t$ seconds the velocity of the particle is $v$ m s$^{-1}$
The following horizontal forces act on the particle:
β’ a constant driving force of magnitude 1.8 newtons
β’ another driving force of magnitude $30\sqrt{t}$ newtons
β’ a resistive force of magnitude $0.08v^2$ newtons
When $t = 70$, $v = 54$
Use Euler's method with a step length of 0.5 to estimate the velocity of the particle after 71 seconds.
Give your answer to four significant figures.
[6 marks]
\hfill \mbox{\textit{AQA Further Paper 1 2021 Q8 [6]}}