{title2=$v=|\mathbf v|$}
{wiki}

<Speed> is the nonnegative magnitude of <velocity>, a <scalar> rather than a <vector>. In orthonormal <Cartesian coordinates>,
$$
v(t)=|\mathbf v(t)|=\sqrt{v_x(t)^2+v_y(t)^2+v_z(t)^2}.
$$
Its <SI> unit is $\mathrm{m/s}$. In the reversal example under <velocity>, the endpoint <velocities> $-2\,\mathrm{m/s}$ and $+2\,\mathrm{m/s}$ both have <speed> $2\,\mathrm{m/s}$, but the <speed> falls to zero between them. A <speed> reading alone therefore cannot tell which way the body is moving.

For a smooth path, the total distance traveled is its <arc length>, $L=\int_{t_1}^{t_2}v(t)\,dt$. Unlike the <integral> of a signed <velocity> component, this <integral> cannot cancel outward and return motion. The reversal example travels $2\,\mathrm m$ in $2\,\mathrm s$, giving an average <speed> of $1\,\mathrm{m/s}$, while its average <velocity> is zero. This makes <speed> useful for estimating travel duration or fuel use, while <velocity> also tracks progress toward a destination. https://openstax.org/books/university-physics-volume-1/pages/3-2-instantaneous-velocity-and-speed[Ling, Sanny and Moebs, section 3.2: distance traveled versus displacement]{ref}


 Speed (source code)