hydr
Sep18-08, 11:04 PM
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...
\intdv/(250-v) = \intkdt 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.
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...
\intdv/(250-v) = \intkdt 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.