A curve has parametric equations $x={{t}^{3}}$, $\quad$ $y={{t}^{4}}-18{{t}^{2}}$, $\quad$ f

Question

A curve has parametric equations $x={{t}^{3}}$, $\quad$ $y={{t}^{4}}-18{{t}^{2}}$, $\quad$ for $t>0$. Find the equation of the tangent to the curve where it is parallel to the $x$-axis.[4] Hence determine whether this tangent will meet the curve again.[2] 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. On a separate diagram, sketch the displacement-time graph.[2] Find the time period when the particle is moving away from the fixed point.[2]

Accepted Answer

(a)(i) $y=-81$ (b)(ii) $0\le t<2$ or $t\ge 5$

2022 NYJC Promo Q8

2022 NYJC Promo Q8

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