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Author Topic: acceleration in a velodrome  (Read 629 times)  Share 

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  • Victorian
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acceleration in a velodrome
« on: June 03, 2008, 03:33:02 pm »
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Question 19
A cyclist accelerates uniformly from rest up to a speed of 15 m s-1. He completes two laps of a small velodrome as he does this. Which of the following is the best estimate of his speed at the end of the first lap?

A   8 m s-1
B   9 m s-1 
C   10 m s-1
D   11 m s-1
E   12 m s-1


The answer is below:
D

But I don't understand how it works!

enwiabe

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Re: acceleration in a velodrome
« Reply #1 on: June 03, 2008, 04:18:32 pm »
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It says two laps. So you can assume that you have 1 lap = to a distance of 1s, and two laps = to a distance of 2s.

For the full two laps:
x(distance) = 2s
u = 0 m/s
v = 15 m/s
a = a

For 1 lap:
x = s
u = 0
v = v
a = a

For lap no. 1:
v^2 = u^2 + 2as
v^2 = 0^2 + 2as
      = 2as

For lap no. 2:
v^2 = u^2 + 2as
225 = 0^2 + 2*a*2s = 4as
therefore, 4as = 225 and 2as = 225/2

v^2 = 2as = 225/2

v = sqrt(225/2) ~ 10.6 ~ 11 m/s

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Re: acceleration in a velodrome
« Reply #2 on: June 03, 2008, 04:48:06 pm »
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Thanks enwiabe! I think that's quite a strange answer