2022 NYJC Promo Q8
(a)
A curve has parametric equations
$x={{t}^{3}}$, $y={{t}^{4}}-18{{t}^{2}}$, for $t>0$.
(i) Find the equation of the tangent to the curve where it is parallel to the $x$-axis.
[4]
(ii) Hence determine whether this tangent will meet the curve again.
[2]
(b)
A particle moves in a straight line. Initially, it has a displacement of $-5$ units from a fixed point and it passes through the same fixed point at $t=5$. It is momentarily at rest when $t=2$. The graph shows the velocity-time graph of the particle.
(i) On a separate diagram, sketch the displacement-time graph.
[2]
(ii) Find the time period when the particle is moving away from the fixed point.
[2]
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