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In introductory kinematics, how do you find the magnitude of the average acceleration of an object over a time interval , given its initial velocity and final velocity in one dimension?
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and the magnitude is .
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Identify the given quantities: initial velocity \(v_i\), final velocity \(v_f\), and the time interval \(\Delta t\) over which the change occurs.
Recall the definition of average acceleration \(a\) as the change in velocity divided by the time interval:
\[a = \frac{v_f - v_i}{\Delta t}\]
Calculate the difference in velocity by subtracting the initial velocity from the final velocity:
\[\Delta v = v_f - v_i\]
Divide the velocity change \(\Delta v\) by the time interval \(\Delta t\) to find the average acceleration:
\[a = \frac{\Delta v}{\Delta t}\]
To find the magnitude of the average acceleration, take the absolute value of \(a\):
\[|a| = \left| \frac{v_f - v_i}{\Delta t} \right|\]