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Answer:
the maximum possible constant speed is 8 m/sec
Explanation:
from the image, Given that
r(t) = (2t, t²,t²/3), -5 ≤ t ≤ 5
Given that the curvature K(t) = 2 / ( t² + 2)²
note that t² + 2 ≥ 2
(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 = ║v(t)║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
Answer:
a)
reaction time = 0.70 s
distance travelled in reaction time = v*t
= 20 m/s * 0.70 s
= 14 m
So, when brake is applied, distance remaining= 110 m - 14 m = 96 m
Answer: 96 m
b)
vf = 0 m/s
d = 96 m
vi = 20 m/s
use:
vf^2 = vi^2 + 2*a*d
0 = 20^2 + 2*a*96
-400 = 2*a*96
a = -2.08 m/s^2
Answer: -2.08 m/s^2
c)
use:
vf = vi + a*t
0 = 20 - 2.08*t
t = 9.6 s
Answer: 9.6 s
Explanation:
Answer:
0.14594 g/cm³
Explanation:
Density = Mass / Volume
Mass = 5400 g
Volume = 0.37 m³
Density = M /V
volume = 0.37 m³ = 37000 cm³
Density = 
= 0.14594 g/cm³