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?

Answer 1

#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)#
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Answer 2

To find the average acceleration, you can use the formula:

Average acceleration = (change in velocity) / (time interval)

First, calculate the change in velocity: Change in velocity = final velocity - initial velocity

Then, find the time interval, which is given as 2 seconds.

After that, substitute the values into the formula: Average acceleration = (6 m/s east - 8 m/s south) / (2 seconds)

Now, subtract the velocities: Change in velocity = (6 m/s east - 8 m/s south) = 6 m/s east + 8 m/s south

Finally, divide the change in velocity by the time interval: Average acceleration = (6 m/s east + 8 m/s south) / 2 seconds

This gives you the average acceleration.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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