# A cyclist moving on a level road

1. Aug 25, 2012

### norhh

1. The problem statement, all variables and given/known data

a cyclist is moving on a level road at 4m/s stops pedaling and lets 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. Relevant equations

3. The attempt at a solution

2. Aug 25, 2012

### uart

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

$$\frac{dv}{dt} = -f(v)$$
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. Aug 26, 2012

### norhh

yes after that i do not know what to do

4. Aug 26, 2012

### uart

Rewrite it as:

$$\frac{dt}{dv} = \frac{-1}{f(v)}$$

and integrate.

5. Aug 26, 2012

### Ray Vickson

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

RGV

6. Aug 26, 2012

### vela

Staff Emeritus