The position of a particle moving along the \( \mathrm{x} \)-axis is given by \( x(t)=t^{3}-9 t^... VIDEO
The position of a particle moving along the \( \mathrm{x} \)-axis is given by \( x(t)=t^{3}-9 t^{2}+24 t \) meters where \( t \) is in seconds, \( t \geq 0 \).
(a) Draw sign diagrams for the particles velocity and acceleration functions.
(b) At what times is the particles: (a) speed decreasing (b) velocity decreasing?
(c) Find the total distance by the particle in the first 5 seconds of motion.
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