Mechanics/ Maths Question

dmg24

Evening all,

I'm having to do a module in Mechanics, even though I am adamant I'll never teach it. I've been at it all day (Maths, that is ) and I am stuck on the last question:

A cyclist is freewheeling down a long straight hill. The times taken between successive kilometre posts are 100 seconds and 80 seconds. Assuming her acceleration is constant, find this acceleration.

I can picture in my head what I should be doing, I just can't write it down!

Any help gratefully received. I'll make the hot chocolate ... x

melancholly

hmm... maybe some simultaneous equations?

you don't have u and v (or u1 and v1 for km1 and u2 and v2 for km2), but you know v1 = u2...... and v = u + at... does that sound like the right track?

melancholly

i can't seem to remove all the unknowns that way....... hmm... this must be (relatively!!) obvious but i can't see it!

dmg24

Yep, I was thinking simultaneous equations, or substituting one into the other. It does look really obvious, but I have pages of nonsense (including some pretty sexy diagrams!), but still no closer to an answer ...

My problem is I have no spacial awareness ... distance and speed mean nothing to me! x

melancholly

maybe one equation should be for one kilometer and one should be for the whole 2km stretch?

melancholly

i am stumped............

dmg24

You're not going to believe this. I have just done a Google, and found this ...

http://www.hostfeel.com/science/2499-2-science.html

Am going to have to print it off and have a read ... far too much to follow on screen!

Thanks for having a go ... let me know if you agree with the answer! x

dmg24

Have just realised there are three different answers on that link - I am agreeing with the first, that the answer is 1/36?

The other two seem too simplistic (and the above makes a lovely se)? My only concern is that the above does not seem to substitute back in to the other equations ...

Or do I just need sleep?!!

melancholly

yeah - d'oh!

i can't deal with such huge numbers so for the first equation i had u = 50a - 10 and for the second u = 90a - 100/9

so that goes to 40a = 10/9 and a=1/36


i guess we had the right idea, but the wrong equation!

time for some sleep now!

Labman_2

Same question is here:
-
http://assets.cambridge.org/052154/9000/sample/0521549000ws.pdf

...bad news is answer is missing...good news is that it (hopefully!) explains how to work it out!

dmg24

Fantastic, am glad to see someone agrees (I used my calculator for the biggies!).

I'm going to ignore that it does seem to go back in to the other equations, and pretend they are all wrong, so we must be right. Ignorance is bliss!

I'll no doubt be back tomorrow for the next chapter ...

Thanks mc x