- #1

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## Main Question or Discussion Point

Force is equal to change in potential (r is a point in space suppose integrating between points r1 to r2 in time t1 to t2, i did not indicate this but it is not relevant for my quenstion:

[tex]mr'' =F(r) = -\delta V[/tex]

after multiplying both sides by dr it is obvious RHS will give potential difference, but LHS needs to be transformed to show corresponding kinetic energy difference:

[tex]mr'' \cdot dr = m \int_{}^{} r'' \cdot r' \cdot dt = m \int_{}^{} \frac{d}{dt}r' ^{2}dt [/tex]

:(

The problem is there should be a 1/2 term there as well. I don't know how to integrate this LHS. Can you please help- show me clearly step by stem what is done and where this 1/2 comes in...

[tex]mr'' =F(r) = -\delta V[/tex]

after multiplying both sides by dr it is obvious RHS will give potential difference, but LHS needs to be transformed to show corresponding kinetic energy difference:

[tex]mr'' \cdot dr = m \int_{}^{} r'' \cdot r' \cdot dt = m \int_{}^{} \frac{d}{dt}r' ^{2}dt [/tex]

:(

The problem is there should be a 1/2 term there as well. I don't know how to integrate this LHS. Can you please help- show me clearly step by stem what is done and where this 1/2 comes in...