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1.10 G: Differentiation

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Question 207

The altitude hhh (in meters) of a specialized research drone during a 10-second test flight is modeled by the function

h(t)=t3−kt2+15t−12 h(t) = t^3 - kt^2 + 15t - 12 h(t)=t3−kt2+15t−12

where t t\,t is the time in seconds (0≤t≤100 \le t \le 100≤t≤10) and k k\,k is a constant.

a.

Find, in simplest form, (i) h′(t)h'(t)h′(t) (ii) h′′(t)h''(t)h′′(t)

[2]
b.

The curve with equation v=h′(t)v = h'(t)v=h′(t) (velocity) intersects the curve with equation a=h′′(t)a = h''(t)a=h′′(t) (acceleration) at the points P P\,P and QQQ.

Given that the ttt-coordinate of P P\,P is 5,

find the value of kkk.

[2]
c.

Hence find the coordinates of QQQ.

[4]
Markscheme

1.10 G: Differentiation Questions

  1. A Level
  2. /Maths
  3. /1.10 G: Differentiation

375 exam-style questions on AQA A Level Maths 1.10 G: Differentiation, covering 1.10.1 The derivative and second derivative, 1.10.2 Differentiating standard functions, 1.10.3 Applications of differentiation, 1.10.4 Product, quotient and chain rules (A-level only), 1.10.5 Implicit and parametric differentiation (A-level only), and 1.10.6 Constructing differential equations (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.

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