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Rates of change and differential equations — Question 12

QCAA 2025, Paper 2 · 7 marks

Q12 · 2025 · Technology-activeSimple familiar7 marks

QUESTION 12 (7 marks)

A 10 kg object is travelling at ground level with a constant velocity.
At an instant, two forces of 60 N and 42 N act simultaneously on the object parallel to the ground in the directions shown.
Let unit vectors in the east and north directions be i^\hat{\mathbf i} and j^\hat{\mathbf j} respectively.
Force diagram with a 42 N force at 18 degrees north of east and a 60 N force at 32 degrees south of west.
a)
Determine the resultant force acting on the object expressed in Cartesian form. Simplify your answer.
[2 marks]
b)
Determine the acceleration of the object after the forces act. Leave your answer in Cartesian form.
[1 mark]
c)
The object is initially travelling at 5 m s−15\text{ m s}^{-1} in a northerly direction when the forces act. Determine an expression for the object’s velocity in terms of time, tt, after the forces act. Leave your answer in Cartesian form.
[2 marks]
d)
Calculate the speed of the object after the forces have been acting for two seconds.
[2 marks]
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