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Rates of change and differential equations — Question 17

QCAA 2024, Paper 1 · 6 marks

Q17 · 2024 · Technology-freeComplex familiar6 marks

QUESTION 17 (6 marks)

The acceleration (m s−2^{-2}) of an object that moves in a straight line in an easterly direction over time tt for 0≤t≤π60\le t\le\frac{\pi}{6} seconds is given by a=2(1+v2)a=2(1+v^2), where vv is its velocity (m s−1^{-1}). The object is initially at rest at a position that is ln⁡(2)\ln(\sqrt2) metres west of the origin. A student uses this information to calculate that the object is positioned at the origin when t=π6t=\frac{\pi}{6} seconds. Evaluate the reasonableness of the student’s calculation.
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