Find the boat's speed as a function of time

[khdani]

Hello,
I don't know if I do it right, if someone please verify me, Thank You.

Given a boat with mass 'm' and travelling with speed V_m.
There are two forces acting on the boat. The force of water resistance which is
dependent on boat's speed relatively to the water and given by
$$\vec{f}$$=-bv²
and the force of the engine. Assume that the motion is linear and the water
is stationary. In order to stop the boat the engine rotation direction is reversed.
a)Find the motion equation
b)Find the engine force
c)Find the boat's speed as a function of time
-------
a)
fw-water resistance force
f - engine force
$$\Sigma$$F=ma
V²=V₀² - 2*a*X
V₀=V_m
V=0
=>V_m²=2*a*X =>
X=V_m²/2*a => X=V_m²/m*2*(fw+f)

b)
V=V₀-a*t => V_m=a*t =>
V_m=(f+fw)*t/m
f = Vm*m/t-fw

c)
V=V₀+a*t=V_m-(f+fw)*t/m

 

[JoAuSc]

This problem seems a little bit ambiguous. Do you need the equation of the boat's motion before it stops, as it's stopping, or for both? Is this a freshman-level physics problem, or intermediate (where you deal with differential equations)?

 

[borgwal]

Most of the equation you wrote down you can't use: those are all based on a constant acceleration. You don't have a constant acceleration here as a depends on v! So, your answers to a, b, and c are all incorrect.