# How to find average acceleration? a bird is flying south at 8 m/s. the bird veers and changes velocity to 6 m/s east over a 2 second period. What is the average acceleration (magnitude and direction) during this 2 second interval?

##abs(vec a) = 5 m/s^2 ##

## theta = arctan (4/3)##

by definition average acceleration over time ##t## is:

##vec a = (Delta vec v)/(t) = 1/t (vec v_2 – vec v_1)##

using W-E as positive Cartesian x-direction and S-N as positive y direction, we have

##vec v_1 = ((0),(-8)), qquad vec v_2 = ((6),(0))##

##implies vec a = 1/2( ((6),(0)) – ((0),(-8)) )= 1/2 ((6),(8)) = ((3),(4))##

##implies vec a = ((3),(4))##

from that we can calculate the magnitude of the average acceleration as

##abs(vec a) = sqrt(3^3 + 4^2) = 5 m/s^2 ##

it’s direction, where ##theta## is measured positive anti clockwise from the x-axis is

##tan theta = 4/3, theta = arctan( 4/3)##