A cyclist moving on a level road

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In summary, you can integrate to find the total retardation, but you do not know what to do after that.
  • #1
norhh
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Homework Statement



a cyclist is moving on a level road at 4m/s stops pedaling and let's the wheels comes to rest the retardation of cycle has 2 components a constant 0.08m/s^2 due to friction in working parts and resistance of 0.02v^2/m where v is speed in m/s and distance tranversed by the cycle before it comes to rest.(log 5=1.6)

2. Homework Equations



The Attempt at a Solution

 
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  • #2
norhh said:

Homework Statement



a cyclist is moving on a level road at 4m/s stops pedaling and let's the wheels comes to rest the retardation of cycle has 2 components a constant 0.08m/s^2 due to friction in working parts and resistance of 0.02v^2/m where v is speed in m/s and distance tranversed by the cycle before it comes to rest.(log 5=1.6)

You understand that this is a differential equation right. You need to write an equation in the form:

[tex]\frac{dv}{dt} = -f(v)[/tex]
Are you able to write this equation? This is your starting point.BTW. f(v) here is the total retardation as a function of velocity.
 
  • #3
yes after that i do not know what to do
 
  • #4
norhh said:
yes after that i do not know what to do

Rewrite it as:

[tex]\frac{dt}{dv} = \frac{-1}{f(v)}[/tex]

and integrate.
 
  • #5
norhh said:
yes after that i do not know what to do

Are you saying you do not know how to solve a differential equation?

RGV
 
  • #6
norhh said:

Homework Statement



a cyclist is moving on a level road at 4m/s stops pedaling and let's the wheels comes to rest the retardation of cycle has 2 components a constant 0.08m/s^2 due to friction in working parts and resistance of 0.02v^2/m where v is speed in m/s and distance tranversed by the cycle before it comes to rest.(log 5=1.6)

2. Homework Equations



The Attempt at a Solution



norhh said:
yes after that i do not know what to do
Per the forum rules, you need to show more effort to receive help here.
 
  • #7
finally got it thanks
 

Related to A cyclist moving on a level road

1. How does the cyclist maintain balance while riding on a level road?

The cyclist maintains balance by continuously making small adjustments with their body and handlebars to counteract any changes in direction or weight distribution. They also rely on their bike's gyroscopic stabilizing effect and their own sense of balance.

2. What factors affect the speed of a cyclist on a level road?

The speed of a cyclist on a level road is affected by factors such as their fitness level, the weight and aerodynamics of their bike, the condition of the road, wind conditions, and the grade of the road (even a slight incline can affect speed).

3. How does a cyclist deal with changing terrain on a level road?

A cyclist must adjust their pedaling cadence and gear selection to maintain a consistent speed on changing terrain. They may also need to shift their weight and adjust their body position to maintain balance and control.

4. How does drafting affect a cyclist's speed on a level road?

Drafting, or riding closely behind another cyclist, can significantly increase a cyclist's speed on a level road. This is because the lead cyclist creates a slipstream that reduces air resistance for the following cyclist, allowing them to conserve energy and maintain a higher speed.

5. How does a cyclist's position on the bike affect their performance on a level road?

A cyclist's position on the bike can greatly affect their performance on a level road. A more aerodynamic position, such as tucking in and lowering the head, can reduce air resistance and increase speed. Additionally, a proper bike fit and body position can improve power transfer and avoid strain and discomfort during long rides.

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