Position vectors as a function of time
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The path of a particle with respect to the origin is described as a function of time \(t\), by the vector equation
\[r(t)=\left(t^2-4\right) i+2 t j,\quad t \geq 0\]
i) Find the cartesian equation of the path.
ii) Sketch the path of the particle.
iii) Find the time at which the particle crosses the \(y\)-axis.
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