A particle moves along a straight line from $O$. Its displacement after $t$ seconds is \(s=\dfra

Question

A particle moves along a straight line from $O$. Its displacement after $t$ seconds is $s=\dfrac14t^4-3t^3+9t^2$ metres, where $0\leq t\leq6$. (i) Find an expression for the velocity of the particle in fully factorised form. (ii) Find the positive times at which the particle is instantaneously at rest. (iii) Show that the particle is accelerating when $t=4$.

Accepted Answer

(i) $v=t(t-3)(t-6)\text{ m s}^{-1}$ (ii) $t=3\text{ s},\ 6\text{ s}$ (iii) At $t=4$, $v=-8\text{ m s}^{-1}$ and $a=-6\text{ m s}^{-2}$, so the particle is accelerating

Quartic displacement and acceleration

Quartic displacement and acceleration

Solution:

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