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Rates of change and differential equations — Question 13

QCAA 2025, Paper 1 · 5 marks

Q13 · 2025 · Technology-freeSimple familiar5 marks

QUESTION 13 (5 marks)

The velocity (m s−1^{-1}) of a 3 kg object moving in a straight line is given by v=2cos⁡−1(x3),0≤x<3,v=2\cos^{-1}\left(\frac{x}{3}\right),\qquad0\le x<3, where xx is its position (m) from the origin.
a)
Determine the momentum (kg m s−1^{-1}) of the object when it is at the origin.
[2 marks]
b)
Determine the acceleration (m s−2^{-2}) of the object when it is at the origin.
[3 marks]
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