Ok heres my problem: The acceleration of a car is proportional to the difference between 250 km/h and the velocity of the car. If this machine can accelerate from rest to 100 km/h in 10s, how long will it take for the car to accelerate from rest to 200 km/h? Here is what ive done so far: dv/dt = k(250-v) integrating that... [tex]\int[/tex]dv/(250-v) = [tex]\int[/tex]kdt which equates to -ln|250-v| = kt + c solving for v gives me v = e^c * e^(-kt) - 250 Now, i proceeded to solve for k, making e^c = 1 since i assumed c = vnaught and vnaught = 0 When i solved for t i ended up getting like 7.2 seconds which isnt right if it takes 10 seconds to accelerate to 100 km/h. My main question is: how do i equate vnaught into the equation? Because obviously i was mistaken to think vnaught = c. I have also tried to make e^c = B, but once again am stuck as to how to equate B to vnaught. Any suggestions would be helpful, my book doesnt really explain much.