The velocity, vvv m s−1\text{m s}^{-1}m s−1, of a research drone at time ttt seconds (t>0t > 0t>0) is defined such that its acceleration aaa follows the equation:
a=dvdt=12t+kt3+10 a = \frac{dv}{dt} = \frac{12}{\sqrt{t}} + \frac{k}{t^3} + 10 a=dtdv=t12+t3k+10where kkk is a constant.
It is observed that the rate of change of the drone's acceleration is zero at the instant where t=4t = 4t=4.
Determine the value of kkk.
Given that the drone's velocity is 100100100 m s−1\text{m s}^{-1}m s−1 when t=1t = 1t=1, find an expression for vvv in terms of ttt, giving each term in simplest form.
Practise Edexcel A Level Maths Differentiation with exam-style questions for A Level Maths. 311 questions covering 9.1 Differentiating sin x and cos x, 9.2 Differentiating exponentials and logarithms, 9.3 The Chain Rule, 9.4 The Product Rule, 9.5 The Quotient Rule, 9.6 Differentiating Trigonometric Functions, 9.7 Parametric Differentiation, 9.8 Implicit Differentiation, 9.9 Using Second Derivatives, and 9.10 Rates of Change, matched to the Edexcel A Level Maths (9MA0) specification and written in Paper 1, Paper 2 and Paper 3 style. Every question includes a full worked solution and mark scheme, so you can see where marks are awarded rather than just whether you got the answer right.
