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velocity is the derivative of position; yes the change of distance with respect to time/parameter

yeah
ds/dt = v

differejntiate it again

a=dv/dt so a = d2v/dv2

so i should take the derivative of the velocity function?

what is curvature :)

the change in direction with respect to distance :)

no its the beauty of jennifer aniston..lol

yeah a=dv/dt

does your s(t) there indicate position of speed?

position as a function of time

yeah its right

the derivative of velocity as part of acceleration.... if you do vectors

a = d^2s/dt^2. + k(ds/dt)^2