Part 4/5:
Utilizing graphing calculators or software, we can represent the motion of the particle through a distance versus time graph. The graphical output illustrates how the particle moves, highlighting moments of rest and changes in velocity.
The curve will clearly show the points at which the particle is at rest (where the slope of the curve is zero) at ( t = 1 ) and ( t = 3 ) seconds.
The highest point of the graph corresponds to the maximum distance achieved within the analyzed time frame.
Total Distance Traveled
To compute the total distance traveled by the particle over a specified time interval, one must consider the distances traveled in segments.
- Calculate ( s(1) ):
[
s(1) = 3(1)^2 - 12(1) + 9 = 0 \text{ m}
]
- Calculate ( s(5) ):
[