Acceleration Dependent on Velocity

[mickeylutz]

A constant Force F is applied by the engine of a stationary car causing it to move to the right. Opposing force F, is a force of magnitude -kv, where k is a constant and v is the velocity of the car. The car has a mass of m.

a) Determine the horizontal acceleration in terms of k, v, F and m

b)Derive the equation expressing the velocity of the car as a funtion of time t in terms of k, F, and m.I tried using F=ma:

F-kv=ma
a= (F-kv)/m

Then I integrated this from 0 to t and got

v=(F-kv)t/m

I know that these answers can't be right, since this would be the same result if I had used the equation for constant acceleration. And its not constant acceleration, I'm not sure how to do this.

Thanks!

 

[Fredrik]

When you integrate the velocity with respect to time, the result isn't velocity multiplied by time.