Answer:
320 N/m
Explanation:
F = k·Δx
where
F is the restoring force of the spring
k is the proportionality constant called the ‘spring constant’
Δx is the change in the spring’s position due to the deformation.
You need the k so
25 cm= 0.25m
k=F/∆x = 80/0.25 = 320 N/m
Answer:
We first to know that if the wheel rotates from rest means that at t=0 the velocity and the angle rotated is 0.
Then, we know:

Integrating 2 times, we have:

For the first 27.9 s, we have:
w = 37.107 rad/s
angle = 517.6426 rad
For the next seconds, according to the text, the angular velocity is constant so
w = 37.107 rad/s and hence, integrating:

Then, the time remaining is:
53.5 - 27.9 = 25.6
So for the next 25.6 seconds we have:

Finally, we add the 2 angles and we have as a result:

“to predict the speed that a coaster will reach before it is ever placed on the track. ... When coaster goes up by height h then its gravitational potential energy increases by the amount m.g.h where m = mass of coaster, h = height of coaster and g = gravitational acceleration due to Earth”