Instantaneous power
= Instantaneous power
{title2=$P(t)=\mathbf F(t)\cdot\mathbf v(t)$}
<Instantaneous power> is <power> at a particular moment. Consider a <point mass> with <mass> $m=2\,\mathrm{kg}$, initially at rest, acted on by a constant net <force> $F=3\,\mathrm N$ along a straight path. <Newton's second law> gives constant <acceleration> $a=F/m=1.5\,\mathrm{m/s^2}$, hence <velocity> $v(t)=at$ and
$$
P(t)=Fat=(4.5\,\mathrm{W/s})t.
$$
The <instantaneous power> starts at zero even though the <force> is nonzero, because the initial <velocity> is zero. At distance $4\,\mathrm m$, the <kinetic energy> example below gives <speed> $\sqrt{12}\,\mathrm{m/s}$, so the final <instantaneous power> is $3\sqrt{12}\,\mathrm W\approx10.3923\,\mathrm W$. Negative <instantaneous power> means the selected <force> is removing <energy> at that moment.