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Question 560

The altitude of a specialized research probe, H(t)H(t)H(t) in kilometres, is modelled for time t>0.5 t > 0.5\,t>0.5 seconds using its vertical acceleration.

It is given that:

  • the acceleration is H′′(t)=12t2+2t2H''(t) = 12t^2 + \dfrac{2}{t^2}H′′(t)=12t2+t22​
  • the point P P\,P on the graph of altitude against time has a ttt-coordinate of 1
  • the tangent to the graph of H(t)H(t)H(t) at P P\,P has the equation H=8t−3H = 8t - 3H=8t−3
a.

Determine the equation of the normal to the graph of altitude against time at the point PPP. Give your answer in the form at+bH+c=0at + bH + c = 0at+bH+c=0, where a,b, a, b,\,a,b, and c c\,c are integers.

[3]
b.

Find an expression for H(t)H(t)H(t) in terms of ttt.

[7]
Markscheme

Integration Questions

  1. A Level
  2. /Maths
  3. /Integration

864 exam-style questions on Edexcel A Level Maths Integration, covering 11.1 Integrating Standard Functions, 11.2 Integrating f(ax + b), 11.3 Using Trigonometric Identities, 11.4 Reverse Chain Rule, 11.5 Integration by Substitution, 11.6 Integration by Parts, 11.7 Partial Fractions, 11.8 Finding Areas, 11.9 The Trapezium Rule, 11.10 Solving Differential Equations, and 11.11 Modelling with Differential Equations. Each one has a worked solution and a mark scheme showing where the marks go.

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