What are some good equations to find acceleration?

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Key equations for finding acceleration include Newton's second law, f = ma, and the relationships involving distance, velocity, and time. Acceleration can be expressed as a = d(v)/dt, indicating it is the derivative of velocity with respect to time. Additionally, acceleration is the second derivative of distance, d, with respect to time. In vector form, acceleration is represented as \vec a = \frac{dv_x}{dt} i + \frac{dv_y}{dt} j + \frac{dv_z}{dt} k, where i, j, and k are unit vectors in the x, y, and z directions, respectively. These equations provide a comprehensive understanding of how to calculate acceleration in various contexts.
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what are some good equations to find acceleration?
 
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Let d = distance, v = velocity and a = acceleration
Then v =d(d)/dt
and
a = d(v)/dt
a = second derivative of d.
 
\vec a= \frac{dv_x}{dt} i +\frac{dv_y}{dt}j +\frac{dv_z}{dt}k

wherei, j, k are unit vectors along x,y and z directions
 
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Thanks for the help

thanks for helping me.
 
I have recently been really interested in the derivation of Hamiltons Principle. On my research I found that with the term ##m \cdot \frac{d}{dt} (\frac{dr}{dt} \cdot \delta r) = 0## (1) one may derivate ##\delta \int (T - V) dt = 0## (2). The derivation itself I understood quiet good, but what I don't understand is where the equation (1) came from, because in my research it was just given and not derived from anywhere. Does anybody know where (1) comes from or why from it the...
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