AbrahamPhysics

The Acceleration Function

The acceleration function is the time-deravitive of the velocity function. Again, while there are many ways to write this mathematically, the fundamental relationship between the acceleration and the velocity is better to remember in words. Once you know this definition, regardless of the form of the velocity function, you can find the acceleration by taking the derivative with respect to time.

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Graphical Representation of Acceleration, Velocity, and Position

Let's look at the graphcial representation of the acceleration, velocity, and position all together. This gives us added insight in how the three quanties are related and different.

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Average acceleration

The average acceleration is defined the same way the average velocity was defined. Take two points in time, \(t_i\) and \(t_f\), where \(\Delta t = t_f- t_i\). Calculate or determine the velocities at those two times, \(v(t_i)\) and \(v(t_f)\), where \(\Delta v = v(t_f)- v(t_i)\). The average acceleration in one dimension is given by: $$a_{avg} = \frac{\Delta v}{\Delta t}$$