How Does Power Affect Car Acceleration with Air Resistance?

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The discussion focuses on a physics problem involving a car's acceleration affected by power and air resistance. The car, with a mass of 720 kg, has a constant engine power of 81 kW and experiences resistance proportional to its speed. Part (a) requires demonstrating that the car's speed satisfies a specific differential equation, while part (b) asks for a general expression for time in terms of speed and the evaluation of the time taken to accelerate from 5 m/s to 20 m/s. The user initially struggles with finding the constant of integration due to a lack of initial conditions but later realizes that the problem specifies taking the initial speed as 5 m/s. The discussion highlights the importance of carefully reading problem statements for necessary information.
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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.
 
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"(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
 
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!
 
Yeh thanks guys, I was being stupid it seems and I spotted it pretty much after posting so it's a-okay :)
 

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