A particle moves along a straight line. Its displacement, $s$ metres, from a fixed point is given

Question

A particle moves along a straight line. Its displacement, $s$ metres, from a fixed point is given by $s=2t^3-15t^2+36t$, where $t$ is the time in seconds and $0\leq t\leq4$. (i) Find the initial velocity of the particle. (ii) Find the times at which the particle is instantaneously at rest. (iii) Determine the intervals for which the particle is decelerating. (iv) Calculate the total distance travelled by the particle in the first $4$ seconds.

Accepted Answer

(i) $36\text{ m s}^{-1}$ (ii) $t=2\text{ s},\ 3\text{ s}$ (iii) $0<t<2$ and $\dfrac52<t<3$ (iv) $34\text{ m}$

Polynomial motion with two reversals

Polynomial motion with two reversals

Solution:

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