Fundamental Mathematics/Calculus/Rate of change

Rate of change

Rate of change

{\frac {\Delta f(x)}{\Delta x}}={\frac {f(x+\Delta x)-f(x)}{\Delta x}}=a

From above,

\Delta f(x)=a\Delta x

\Delta x={\frac {1}{a}}\Delta f(x)

f(x+\Delta x)=a\Delta x+f(x)

For any inclines linear motion, the slope of the line is

{\frac {\Delta v}{\Delta t}}={\frac {v-v_{o}}{t-t_{o}}}=a

\Delta v=a\Delta t

v-v_{o}=a(t-t_{o})

v=a(t-t_{o})+v_{o}

Hence,

v=at

. (

t_{o}=0,v_{o}=0

)

v=at+v_{o}

. (

t_{o}=0

)

v=v_{o}

. (

a_{o}=0

)

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