Long problem sum using Newton second law

[lauraosborn]

Homework Statement

Question is here http://postimage.org/image/som50onyv/

Homework Equations

F=MA

The Attempt at a Solution

for a) Power = force * speed

for b) Force = Mass * Acceleration
F = m * dv/dt

for c) for maximum velocity, there must be zero drag

i am stuck at D and E, so can anyone help me?

 

[clamtrox]

for b) Force = Mass * Acceleration
F = m * dv/dt

so what's the differential equation you get? Remember to include the drag term.

for c) for maximum velocity, there must be zero drag

If there is no drag, then there is no maximum velocity either (the car will just accelerate forever). You should get the answer to this by solving the differential equation you got from b).

 

[LawrenceC]

For part d you have 80000 watts of power available. Thus the car will accelerate until such time that the power consumed by resistance equals the 80000 watts. So what you have to do now is determine the power consumption due to resistance. From that you can determine the value of k.

Hint: Units show you what to equate.

 

[lauraosborn]

for d) i got that k=50

but am stuck for e) again.
m dv/dt = (80000-50v²)/v

thus m v (dv/dx) = (80000-50v²)/v

and thus 1200v (dv/dx) = (80000-50v²)/v

now do i integrate this to find the answer of part e? I'm kinda lost

 

[clamtrox]

Just move all v's to one side and x's to the other side, then integrate. The integral is not completely trivial but it's still doable.