What is the speed of the bicycle?

AI Thread Summary
The discussion revolves around calculating the speed of a bicycle in relation to a car's motion using integration and basic calculus principles. Participants clarify the integration process for velocity and distance, with a focus on the correct application of the fundamental theorem of calculus. There is confusion regarding the integration constants and the correct interpretation of the motion phases, particularly during deceleration. After resolving these issues, one participant concludes that the speed of the bicycle is approximately 9.3 m/s, factoring in its initial position relative to the car. The thread highlights the importance of careful mathematical reasoning in solving physics problems.
  • #51
Never mind, I saw your post.
 
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  • #52
brochesspro said:
Should I take ##C = 12 m## as it is the initial velocity of the body?
The constant of integration in the equation for ##x(t)## doesn't matter, as you are calculating the distance traveled between ##t = 1## and ##t =3##.
 
  • #53
After integration, I got ##x_{t_2}-x_{t_1}=16## after solving and after substituting I got ##x_{t_2}=28m## and thus the speed of bicycle is ##9.3 m/s## as per the question.
 
  • #54
brochesspro said:
After integration, I got ##x_{t_2}-x_{t_1}=16## after solving and after substituting I got ##x_{t_2}=28m## and thus the speed of bicycle is ##9.3 m/s## as per the question.
The bicycle is another ##17m## ahead to begin with. It must be Mark Cavendish after all!
 
  • #55
Oh yeah, so I get the average velocity as ##15 m/s##.
 
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  • #56
Thanks a lot.
So, how do I close this thread?
 
  • #57
brochesspro said:
Thanks a lot.
So, how do I close this thread?
It doesn't need to get closed. It can stay as it is.
 
  • #58
Oh, I see. Thanks again.
 
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