# Dx/dt = dv or just v

#### quasi426

Does dx/dt = dv or just v(avg.)?

Thanks

#### dextercioby

Homework Helper
There's no average,it's the function itself.

$$v(t)=:\frac{dx(t)}{dt}$$

We call it instant velocity,as we can use the definition of the derivative.We compute the "x" comp.of the velocity at the moment of time $t_{0}$ by

$$v(t_{0})=:\lim_{t\rightarrow t_{0}} \frac{x(t)-x(t_{0})}{t-t_{0}}$$

or simply by plugging the time value in the velocity function itself.

Daniel.

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