Question
(a) Calculate the approximate age of the universe from the average value of the Hubble constant, $H_0 = 20\textrm{ km/s}\cdot\textrm{Mly}$ . To do this, calculate the time it would take to travel 1 Mly at a constant expansion rate of 20 km/s. (b) If deceleration is taken into account, would the actual age of the universe be greater or less than that found here? Explain.
1. $15 \textrm{ billion years}$
2. If deceleration has occurred, the average velocity since the beginning of time must be higher, in which case the time is less. The universe would be younger than calculated in part (a).

# OpenStax College Physics for AP® Courses, Chapter 34, Problem 8 (Problems & Exercises)

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This is College Physics Answers with Shaun Dychko. The further away a galaxy is, the faster its receding from us and this is because space itself is expanding and the more space there is between us and this galaxy then the faster it will be expanding or going away from us since there's more space expanding in between. Okay! Now we are going to estimate the age of the universe by saying let's suppose we have to go 1 megalight year and at a speed of 20 kilometers per second, how long would it take to do that? So 1 megalight year is 1 times 10 to the 6 light years and we multiply by speed of light for every l and l represents the speed of light and the y represents a period of a year, which we will convert into seconds so we multiply that by 365.25 days per year and then by 24 hours per day and then 3600 seconds per hour and we now have meters on the top and then we divide that by the speed of 20 kilometers per second converted into meters per second by multiplying by 1000 meters per kilometer, this works out to 4.7305 times 10 to the 17 seconds which I then convert back into years and that is 15 billion years— that's the estimate for the age of the universe. Part (b) says if deceleration is taken into account although it is peculiar that they talk about deceleration since it turns out that in fact the expansion is accelerating— it's getting faster— and that's what dark energy has been postulated to explain not that it really is something that anybody understands but it's just an explanation well... it's gotta be something that makes it expand faster but in any case, the question here says suppose there's deceleration which I think was the original supposition since gravity is expected to, you know, slow down this expansion. So if the average speed is actually higher than what we have got here you know if 20 kilometers per second per megalight year or if 20 kilometers per second is the result of some deceleration in which case, the speed was higher earlier that would make the average velocity higher and by making the denominator bigger, we make this quotient smaller in which case the calculation is off and so the universe is actually younger than what we have calculated.