Part 3/5:
From these calculations, we determine that at ( t = 2 ) seconds the particle is at rest, and at ( t = 4 ) seconds it moves forward at a rate of 12 m/s.
Finding Points of Rest
A particle is considered at rest when its velocity equals zero. To find when this occurs, we set the velocity equation to zero:
[
0 = 6t - 12
]
Solving this equation yields:
[
t = 2 \text{ seconds}
]
To determine if there are additional points of rest, we can apply the quadratic formula to the related distance equation. The solution indicates the particle is at rest at ( t = 1 ) second and ( t = 3 ) seconds.