Friction in driving car We know that friction helps in driving a car, but does this mean that a car can move faster on rough surfaces? Since the coefficient of friction is higher on rough surfaces? 
 A: The coefficient of friction $\mu_s$ might be higher for tires on rough surfaces, yes, but as you said yourself, it is friction $f_s$ that thrusts the car forward.
(And we are talking about static friction throughout, since we are talking about rolling wheels.)
And the coefficient of friction is not equal to friction. High coefficient of friction does not mean high friction.
It only means that there can be high friction. If necessary. It means that if the car starts gripping harder in the asphalt, then the asphalt can hold on. But only if. If the car grips the same amount (if you drive in the same manner)  then you get the same friction, no matter what the coefficient of friction is (as long as it is not too small). 
Mathematically that is shown in the formula for static friction:
$$f_s\lt \mu_s n$$
The friction $f_s$ does not have to rise, when $\mu_s$ is high. It can if it has too, but it doesn't if it doesn't have to. The coefficient of friction (times the normal force) just determines the maximum. That's all. 
A: The friction should be optimum. The cars surely run better on roads than in sand.
The cars have tires so the friction is less and the friction of cars mainly depend on normal force than roads. More rough roads will increase grip during acceleration but as the car starts moving in a constant velocity the roads will grip the tire and drag. Cars will not be fast on rough roads.
The same problem is with F1. Tire gives grip during acceleration but grips road. To improve this Aerodynamics is the answer.
A: There are many types of friction in an automobile...this question dealing with rolling resistance. Most of the heat generated comes from the inertial mass of the vehicle itself and not from the road. Since a paved road is smooth and tires circular there is much less friction on a smooth surface than a rough one so the answer which is also true empirically is no...a rough surface provides far more friction as the tires cannot dissipate the heat nearly as efficiently given weight and the suspension system.
A: I will base my answer on simple rolling motion-
as car starts velocity of center of mass of Tyre reaches v=rw state.
if i press breaks friction acts backward to stop the car.
if i press accelerator friction acts forward to reach v=rw state.
this explanation is high school level more deep discussion requires more insight.
A: There is a maximum fricction force, and is F=uN. u is the coefficient of friction and  N the paralel component of the weight to the normal. 
If the car is at rest, a higher coefficient makes a better accelration. But if the car has a velocity v, only will be a diference between coefficient at a range. If U is the maximu coefficient at that range, coefficients highers than U will not make any diference in the velocity of the car.
