What are the velocity & position of an object as function of time?

[DANIneplanets]

Homework Statement

A motorboat is moving across a lake at a speed vo when its moot suddenly freezes up and stops. The boat then slows down under the frictional force fR = -bv (a) What are the velocity and position of the boat as a function of time? (b) If the boat slows down from 4.0 to 1.0 m/s in 10s how far does it travel before stopping?

Homework Equations

f_r=-bv

The Attempt at a Solution

v=v₀ e^{-b/m *t}
x=x₀+ v₀m/b (1-e ^{-b/m *t})

 

[Nathanael]

Now use the information from part (b) to find the constant b/m

 

[DANIneplanets]

how can i find b/m??

 

[Nathanael]

Put the given information into equations:
v₀e^(-b/m)T = 4 m/s
v₀e^(-b/m)(T+10) = 1 m/s
Then you can find how long it takes to stop (which will depend on v₀)