Why are the directions of frictional forces on the front and rear wheels of a moving car in the opposite direction, when the only the front wheels are accelerated (or only the back wheels)? When the car accelerates, the direction of the static friction exerted by the front wheels on the surface is directed backward. But what about the wheels on the back of the car?
The simplest way to figure out what friction is doing is to see what happens when you turn friction off.
Assume a car on frictionless road.With no friction at all and the car stopped, pushing down on the accelerator makes the rear wheels spin clockwise. They spin on the frictionless surface, the front wheels do nothing, and the car goes nowhere.
Friction on the rear wheels opposes the spinning, so it must point in the direction the car wants to go. For the rear wheels to roll without slipping, the friction must be static.
If we turn on friction to the rear wheels only, the car accelerates forward with the front wheels dragging along the road without spinning. Friction opposes this motion, so it must point opposite to the way the car is going. Again, it must be static friction as tyres roll on roads.
The friction is in opposite directions on front and rear tyres this means torque output from the rear wheels must be greater than certain minimum value for car to move .
Assuming it is a two wheel drive car that is under power with no slipping, one pair of wheels is turned by the drive train to propel the car. The other pair of wheels is turned by the road surface, creating drag. So you have pushing and pulling, static friction in opposite directions.
Why are the direction of frictional forces on the front and rear wheels of a moving car in the opposite direction to what?
Let the direction of the acceleration of the car be $\hat a$ and this could be in the same direction as the velocity of the car (magnitude of velocity increasing) or in the opposite direction to the velocity of the car (magnitude of velocity decreasing).
The frictional force on the bottom of the tyres touching the ground of the driving or braking wheels will be in the direction of the acceleration of the car, ie in the direction $\hat a$, and all the other tyres will have frictional forces opposite to the direction of the acceleration of the car, ie in the direction $-\hat a$.
A variation is when both the accelerator pedal and the brake pedal are being pressed at the same time, or variations of this, when the acceleration is zero which is done when a driver wants to produce smoking tyres, which is sometimes called burnout.
Most easily done on a motorbike because the front and back breaks are controlled independently and the centre of mass of the motorbike and rider can be changed relatively easily.
If the acceleration of the car is then zero with the frictional forces trying to make the car accelerate equal in magnitude but opposite in direction to the frictional forces trying to prevent the car from accelerating.
To understand why the direction of friction is opposite on front and rear wheels, you must take into account the fact that the engine of the car provides torque(turning effect) only to the rear wheels and not to the front wheels. Now,
1-> Let's press the accelerator of the car so that the engine applies a torque on the rear wheels. Note- Torque can only rotate a body and can never produce translational motion. So if the ground is frictionless(in this case friction is the only force that can act horizontally, since friction is absent, so there is no force in horizontal direction and therefore no motion in horizontal direction) , then the rear wheels will rotate about their axel and will not move forward. Note- the wheels will slip in this case.
2-> At the same time, take a look to the front wheels. There is no torque on them(since, the engine apply torque only to rear wheels) and also no net horizontal force since friction is absent(again because, friction is the only force that can act horizontally). So the front wheels are at a standstill, no rotation, no translation.
3-> Now, Let's again press the accelerator but now there is some friction. Same thing happens, the engine apply a torque on the rear wheels, the wheels will rotate(clockwise) and try to slip on the ground. Since, Friction always opposes relative slipping, so it will act such that it prevents clockwise rotation and so it is directed towards right to give a anticlockwise torque. Note that friction acts in forward direction in this case and thus accelerates the car forward.
4-> At the same time, if you look the front wheel, what's happening. The axle of the wheels is moving along with the car and so it pushes the front wheel at its centre, this force by the axle acts at the centre of the wheel so so torque is provided by it,but it give the wheel a forward motion.(Note- there is no torque till now so the wheel are moving forward "without" rotating) Due to this the wheels try to slip. Again friction will act such that it prevents relative slipping. No slipping is only possible if the wheels rotate clockwise along with moving forward. So to prevent slipping friction acts backwards to give a clockwise torque.
Hope it helped! See these posts for a clearer knowledge: Why do rotating bodies have friction between when the surface is accelerating? What is the direction of the frictional force acting on a rolling wheel?