# What is total acceleration?

I'm currently taking a Physics class and we are studying motion in a circular path. and i'm kind of fuzzy on what the total acceleration actually is. take this problem for example

An automobile whose speed is increasing at a rate of 0.700 m/s^2 travels along a circular road with a radius of 20 m. When the instantaneous speed of the automobile is 5.0 m/s, find:

a) the tangential acceleration component

b) centripetal acceleration component.

c) the magnitude and direction of the total acceleration (in respect to the direction of the car.

In this problem, I know the tangential acceleration is what's causing the increase in velocity of the car, the centripetal acceleration is what's causing the car to turn seeking the center. But i have no idea what the total acceleration actually does. what type of effect will it's magnitude have on the car?

$$a_\text{total} = \sqrt{ a_\text{centripetal}^2+a_\text{tangential}^2+2a_\text{centi}\times a_\text{tang} \times \cos \theta }$$
The tangential acceleration is perpendicular to centripetal, $$\cos \theta=0$$, so you can find total acceleration by that formula but $$\cos \theta$$ is zero there.