As a biochemist now teaching physics (middle school), I have what might be two silly questions. I get that for a stationary car to move forward, the forward force (acceleration) needs to be greater than the drag force but QUESTION 1 does the drag force decrease when a car accelerates? I would think it increases as you should experience an increase in air resistance and friction. I also suppose that as long as the acceleration force is greater than the drag force, then the car will move forward. Then QUESTION 2 for that car to slow down, would you see both an increase in the drag force / friction as well as a decrease in acceleration? I suppose if you just take your foot off the accelerator, you will lose just the forward momentum but if you brake, you will add friction to the mix and increase the drag force. This might sound a little simple but I am teaching 11-14 year olds so need to keep it simple :-) Thanks.
Answer 1: The Air drag increases as the car accelerates, the Air drag is usually a complicated expression which can be approximated to be $$F_d=bv$$ where $b$ is a parameter that depends on the the structure or the area of the car, and $v$ is the velocity, The friction or rolling friction in particular doesn't depend on speed, It'll remain constant
Answer 2: if on enough acceleration the drag force equals the the car's force you would attain a constant speed, when you take your foot off the accelerator you would be slowed down by the friction and by the drag force, when you apply the brakes as you said the friction force due to braking will also add to this.
Answer 1:The drag force in the car during the forward acceleration is mainly inertia and friction. The air resistance is taken into consideration only at high speeds. The air resistance will increase due to fluid dynamics but the frictional force will remain constant. Rolling friction is proportional to Weight of the car not the speed and acceleration.
The simple answer is that the drag force will generate whenever an object is accelerated. Justification is Newton's first law of motion.
Answer 2: You have asked whether there is increase in drag force and decrease in acceleration. Your question regarding the acceleration is incorrect.
THERE IS INCREASE IN DECELERATION AND ZERO ACCELERATION. Let us make that point clear. If you take the foot off the accelerator the nature does the work you. If you hit the brakes you add to the natural drag produced due to friction and air resistance to make it fancy.
In both of the cases you loose forward momentum and zero acceleration. You wanted to keep it simple so not mathematical explanation.