# 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?

## 2 Answers

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.

• Put a slightly different way if the seat was not there then relative to the car you would be moving backwards and towards the side of the car. To keep up with the car ie not move relative to ithe car, you need to accelerate forwards and at the same time also accelerate away from the side of the car. – Farcher Feb 20 '16 at 8:26

The total acceleration is the resultant of both tangential and centripetal acceleration so you can find it very easily by vector sum formula

$$a_\text{total} = \sqrt{ a_\text{centripetal}^2+a_\text{tangential}^2+2a_\text{centi}\times a_\text{tang} \times \cos \theta }$$

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.