How far does a bicyclist travel in 30 minutes with a 2:1 gear ratio?

[spikebrdr]

i was wondering if anyone could give me some help with this problem

A bicyclist begins pedaling a bicycle from a complete stop. She accelerates at a constant rate until she is pedaling at 60 revolutions per minute, and then maintains this rate for the remainder of her journey. The bicyclist does not achieve a constant speed until she has been pedaling for 10 minutes. The bike is geared with a 2:1 ratio, meaning that the rear wheel of the bike turns one revolution for every two revolutions of the pedals. How far does the bike travel during a 30-minute duration?

i just need to know how to go about solving the problem and if you could include your answer that would help too.

 

[Grogs]

Are you given the radius of the wheel or the pedals? I don't see how you could come up with a numerical solution without it.

As for the problem, I'd break it up into 2 parts. The first 10 minutes is a constant acceleration problem, while the last 20 minutes is a constant speed problem. You can solve for the speed at ten minutes using the radius of the bike wheel. Use that distance to find the distance traveled in the first 10 minutes and the distance traveled in the next 20 minutes. The total distance traveled will be the sum of these 2 distances.

 

[spikebrdr]

your supposed to assume the radius of the bike wheel. i was going to just make it 1 meter to make it easy.

 

[chronon]

So you're assuming a 2m diameter wheel http://bikekulture.com/cgi-bin/show.cgi?itemlist=&search=Calendars&start=26 . I suppose the low gearing would fit in with this. A typical bicycle wheel diameter would be 700 mm, and I would take 2:1 gearing to mean the wheel went round twice for every revolution of the pedals - that's more typical.