Part 5/5:
s(5) = 3(5)^2 - 12(5) + 9 = 0 \text{ m}
]
The total distance is then calculated from each segment of motion, summing the absolute values of the movements.
If the particle moves up 4 meters to the first maximum, back down 4 meters, and then up to a total distance of 20 meters, the calculations yield:
[
\text{Total Distance} = 4 + 4 + 20 = 28 \text{ meters}
]
This comprehensive analysis demonstrates the crucial role of derivatives in understanding the dynamics of motion. From velocity calculations to points of rest and distance traveled, we see how fundamental calculus is in illustrating real-world phenomena.
Stay tuned for further discussions and illustrations of mathematical solutions!