Suppose you wanted to "pull an Einstein," and create a static universe  in which the gravitational attraction of matter is exac
tly balanced by the gravitational repulsion of dark energy with equation-of-state parameter − 1/ 3 < wq < − 1 and energy density εq.
What is the necessary matter density (εm) required to produce a static universe, expressed in terms of εq and wq?
Will the curvature of this static universe be negative or positive?
What will be its radius of curvature, expressed in terms of εq and wq?
What is the necessary matter density (εm) required to produce a static universe, expressed in terms of εq and wq?
Will the curvature of this static universe be negative or positive?
What will be its radius of curvature, expressed in terms of εq and wq?
2 answers:
You might be interested in
Answer:
a.
b. must be the minimum magnitude of deceleration to avoid hitting the leading car before stopping
c. is the time taken to stop after braking
Explanation:
Given:
- speed of leading car,
- speed of lagging car,
- distance between the cars,
- deceleration of the leading car after braking,
a.
Time taken by the car to stop:
where:
, final velocity after braking
time taken
b.
using the eq. of motion for the given condition:
where:
final velocity of the chasing car after braking = 0
acceleration of the chasing car after braking
must be the minimum magnitude of deceleration to avoid hitting the leading car before stopping
c.
time taken by the chasing car to stop:
is the time taken to stop after braking