Challenging +1.2 This is a variable acceleration problem requiring separation of variables and integration. While it involves a non-standard resistance force with both v and t dependence, the separation is straightforward (√v and (t+1)^2 separate cleanly), and the integrations are routine. The 5-mark allocation and Further Maths context indicate above-average difficulty, but the mathematical techniques are standard calculus without requiring novel insight.
A particle \(P\) of mass 1 kg is moving along a straight line against a resistive force of magnitude \(\frac{10\sqrt{v}}{(t+1)^2}\) N, where \(v\) ms\(^{-1}\) is the speed of \(P\) at time \(t\)s. When \(t = 0\), \(v = 25\).
Find an expression for \(v\) in terms of \(t\). [5]
A particle $P$ of mass 1 kg is moving along a straight line against a resistive force of magnitude $\frac{10\sqrt{v}}{(t+1)^2}$ N, where $v$ ms$^{-1}$ is the speed of $P$ at time $t$s. When $t = 0$, $v = 25$.
Find an expression for $v$ in terms of $t$. [5]
\hfill \mbox{\textit{CAIE Further Paper 3 2021 Q1 [5]}}