Acceleration Dependent on Velocity

AI Thread Summary
The discussion focuses on deriving the horizontal acceleration and velocity of a car under the influence of a constant force and a velocity-dependent opposing force. The acceleration is expressed as a = (F - kv) / m, where F is the applied force, k is a constant, v is the velocity, and m is the mass of the car. The user attempts to integrate this equation to find the velocity as a function of time but realizes the results are incorrect, as they resemble constant acceleration equations. The key issue highlighted is the misunderstanding of integrating velocity with respect to time, emphasizing that the integration process must account for the variable nature of acceleration. Properly addressing these calculations is essential for accurate modeling of the car's motion.
mickeylutz
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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!
 
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When you integrate the velocity with respect to time, the result isn't velocity multiplied by time.
 

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