A small object is dropped from a high altitude and falls vertically towards the ground.
Using a simple model of constant acceleration, a student predicts that the velocity of the object, exactly 5 seconds after being released from rest, is 5g m s−15g\text{ m s}^{-1}5g m s−1. Show how the student has obtained this prediction.
Using a refined model that accounts for air resistance, it is assumed that the object's acceleration, a m s−2a\text{ m s}^{-2}a m s−2, at time ttt seconds after release is given by
a=g−0.2v a = g - 0.2v a=g−0.2vwhere v m s−1v\text{ m s}^{-1}v m s−1 is the velocity of the object at time ttt. Find an expression for vvv in terms of ttt.
Compare the behavior of vvv as t→∞t \to \inftyt→∞ for both models.
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.