How Does Power Affect Car Acceleration with Air Resistance?

[Pronitron]

Homework Statement

A car, of mass 720kg, moves along a straight horizontal road. The engine of the car exerts a constant power of 81kW. The car experiences a resistance to motion which has magnitude 90v N, where v ms^-1 is the speed of the car at time t s
(a) Show that v satisfies the differential equation
900-v^2=8v*dv/dt
(b) Find a general expression for t in terms of v, and hence evaluate the time it takes for the car to accelerate from a speed of 5 ms^-1 to 20 ms^-1

Homework Equations

F=ma

The Attempt at a Solution

So I have done part (a), and I have solved the ODE and got to a point where I have
t+c=-4ln(900-v^2) and I now have no idea how to find the constant of integration, as I can't find any initial conditions lying about in the text, so I'm kinda stuck.

 

[ehild]

"(b) Find a general expression for t in terms of v, and hence evaluate the time it takes for the car to accelerate from a speed of 5 ms^-1 to 20 ms^-1'

You can take t=0 at the instant when the speed is 5 m/s.

ehild

 

[cepheid]

It tells you in part (b) that you should take v(0) to be 5 m/s. That's an initial condition, is it not?

EDIT: Beaten to the punch!

 

[Pronitron]

Yeh thanks guys, I was being stupid it seems and I spotted it pretty much after posting so it's a-okay :)