## 2-2: Instantaneous velocity and speed

Instantaneous velocity:  $v_{_{x}}$  equals the limiting value of the ratio  $\frac{\Delta x}{\Delta t}$  as  $\Delta t$  approaches zero:

$\lim_{\Delta t\rightarrow 0} \frac{\Delta x}{\Delta t}$   (2.4)

In calculus notation, this limit is called the derivative of  $x$  with respect to  $t$  , written $\frac{dx}{dt}$:

 $v_{x}\equiv \lim_{\Delta t\rightarrow 0 }\frac{\Delta x}{\Delta t}=\frac{dx}{dt}$  (2.5)

Instantaneous velocity can be positive, negative, or zero.

Instantaneous speed: of a particle is defined as the magnitude of its instantaneous velocity.

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