Answer:
the maximum possible constant speed is  8 m/sec Â
Explanation:
from the image, Given that
r(t) = (2t, t²,t²/3), -5 ≤ t ≤ 5 Â
Given that the curvature K(t)  = 2 / ( t² + 2)² Â
note that t² + 2 ≥ 2 Â
(t² + 2)² ≥ 4
1 / (t² + 2)² ≤ 1/4
2 / (t² + 2)² ≤ 1/2
Also note that k(0) = 1/2
The normal component of acceleration satisfies aN = kv²
where v = â•‘v(t)â•‘is the speed of the roller coaster.
The maximum possible normal component of acceleration is 32
so, aN ≤ 32 every where on the track
aN = kv² ≤  1/2v² ≤ 32
v² ≤ 64
Therefore, the maximum possible constant speed is  8 m/sec Â
