Speed at any time is called instantaneous speed can be found by differentiating the displacement with respect to time.

${\displaystyle \mathbf {v} =\lim _{\Delta t\to 0}\sum {\Delta x \over \Delta t}}$ ${\displaystyle ={\frac {dx}{dt}}}$

Characteristics

Speed

${\displaystyle v(t)}$

Time

${\displaystyle t}$

Distance

${\displaystyle s(t)=\int v(t)dt}$

Accelleration

${\displaystyle a(t)={\frac {dv(t)}{dt}}}$

Force

${\displaystyle F(t)=m{\frac {dv(t)}{dt}}}$

Work

${\displaystyle W(t)=F\int v(t)dt}$

Energy

${\displaystyle E(t)={\frac {E}{t}}\int v(t)dt}$

Reference

• Motion