If the car just rolls at constant speed as you say, then you are right, there is no acceleration at all:
$$F=m a=0 $$
which means that there is no net force acting on the car at all (Newtons first law of motion). It just continues without disturbance.
But if the car hits the wall... Then there is an acceleration! Actually a deceleration if you wish to call it that (that is, negative acceleration $a<0$). And that acceleration must be (numerically) enormous (let's write it as $a<<0$), since the car is being stopped suddenly by the wall and forced from it's initial speed down to zero speed in a very short time (the time the collision lasts - from the car touches the wall 'till it has been fully stopped - is extremely short).
Then you have (Newtons second law of motion):
$$a << 0 \Rightarrow$$
$$F=m a<<0 $$
and the force that is done on the car to cause this sudden stop is (numerically) extremely large. And the car is whacked.