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Rates of change and differential equations — Question 14

QCAA 2020, Paper 1 · 4 marks

Q14 · 2020 · Technology-freeSimple familiar4 marks

QUESTION 14 (4 marks)

The motion of an object that moves in a straight line is given by v(x)=cos⁡−1(2x)v(x)=\cos^{-1}(2x), where vv is the velocity (m s−1^{-1}) and xx is the displacement (m) from the origin.
a)
Determine a(x)a(x), where aa is the acceleration (m s−2^{-2}) of the object.
[2 marks]
b)
Use the result from 14a) to determine a(0)a(0), given −2π≤a(0)≤0-2\pi\le a(0)\le0. Express your answer in simplest form.
[2 marks]
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