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.
Practise Edexcel A Level Maths 11.11 Modelling with Differential Equations with exam-style questions for A Level Maths. 51 questions, 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.
