If you're driving the car then the centripetal acceleration will result in you being pushed sideways. The tangential acceleration will result in you being pushed back in your seat. So when you combine both accelerations the result is that you are pushed both sideways and backwards at the same time i.e. in a diagonal direction.
Acceleration is a vector, so to combine the centripetal and tangential accelerations you have to add them using vector addition. The result will be a new vector with a magnitude bigger than the centripetal and tangential accelerations and pointing in a direction in between the centripetal and tangential accelerations.
Why normal acceleration doesn't bring a change in speed?
It is, on my view, more fruitful to ask "what is the acceleration vector of an object with uniform (constant speed) circular motion?"
Such an object, moving in the x-y plane has coordinates:
$$x(t) = R\cos(\omega t + \phi)$$
$$y(t) = R\sin(\omega t + \phi)$$
where $R$ (the radius of the circular path) and $\omega$ (the angular speed of the object) are constants. The velocity vector of the object is then
$$\mathbf{v}(t) = -\omega R\sin(\omega t + \phi)\mathbf{\hat{x}} + \omega R\cos(\omega t + \phi)\mathbf{\hat{y}}$$
Clearly, the speed (magnitude of the velocity vector) is constant and equal to $|\mathbf{v}| = \omega R$.
Now, calculate the acceleration vector (do this yourself) and find that (1) it is non-zero and constant in magnitude and, (2) it is perpendicular (normal) to the velocity always.
Best Answer
Acceleration is the general term for a changing velocity. Deceleration is a kind of acceleration in which the magnitude of the velocity is decreasing. The reason this might be confusing is because the word 'acceleration' is sometimes used to mean that the magnitude of the velocity is increasing, to contrast it with deceleration. One cannot go wrong, however, if one always takes acceleration to mean simply 'changing velocity'. In that case, circular motion corresponds to acceleration (because the velocity is changing) but not deceleration (because its magnitude is not decreasing).