Physics Study Guide/Print version - Wikibooks, open books for an open world

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Acceleration

\vec a_{av}\equiv \frac{\vec{v_f}-\vec{v_i}}{t_f-t_i}\equiv \frac{\Delta\vec{v}}{\Delta t}

Acceleration answers the question "Is the object's velocity changing, and if so - how quickly?"

Once again we have an operational definition. We are told what steps to follow to calculate acceleration.

Again, also note that technically we have a definition for AVERAGE acceleration. As for displacement, if we are careful to use a series of small velocity changes, then we can write the definition for INSTANTANEOUS acceleration as

\vec a_{inst}\equiv \frac{\delta\vec{v}}{\delta t}

Or with the help of calculus, we have ...

\vec a_{inst}\equiv \frac{d \vec v}{dt} = \frac{d^2\vec x}{dt^2}