Friction Force and Decelerating Boat

[Arman777]

Homework Statement

A 1000 kg boat is traveling at 100km/h when its engine is shut off.The magnitude of the frictional force $\vec f_k$ between boat and the water is proportional to the speed v of the boat:$f_k=70v$,where v is in meters per second and $f_k$ is in Newtons.Find the time required for the boat to slow to 45 km/h

Homework Equations

$\vec F=m \vec a$
$v-v_0=at$

The Attempt at a Solution

I turned km/h to m/s which its $100km/h=27.7 m/s$ and $45km/h=12.5m/s$
then ;
$ma=-70v$
here the connfusing part is $a$ decreases when v decreases.there's no constant decelaration.I thought integral but without distance I stucked.
$∫mdv=∫-70vdt$

I don't know what to do.

Thank you

 

[Orodruin]

$ma=-70v$
here the connfusing part is $a$ decreases when v decreases.there's no constant decelaration.I thought integral but without distance I stucked.

Indeed the deceleration is not constant. Note that $a = dv/dt$ and so what you have is a differential equation describing how velocity changes with time. You will need to solve this differential equation.

 

[Arman777]

Indeed the deceleration is not constant. Note that $a = dv/dt$ and so what you have is a differential equation describing how velocity changes with time. You will need to solve this differential equation.

I didnt learn diff equation.I am fresman student and uni teaches us second year.Like I have no clue

 

[cnh1995]

.I thought integral but without distance I stucked.
∫mdv=∫−70vdt

That's not the correct equation. You need to separate the variables.
So you can do integrals and differentials separately, right? I guess your only problem is to set up differential equations using the given data?

I didnt learn diff equation.I am fresman student and uni teaches us second year.Like I have no clue

As orodruin pointed out, use a=dv/dt.
What will be the equation of the force on the boat? Which force is acting on it?