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?

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Answer 1 · 2016-08-23T13:25:56

$∣ ∣ \to a ∣ ∣ = 5 \frac{m}{s^{2}}$ $abs(vec a) = 5 m/s^2$

$θ = arctan (\frac{4}{3})$ $theta = arctan (4/3)$

by definition average acceleration over time $t$ $t$ 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

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