What is Velocity vector?

Example 24.3 (A drone in level flight)

A drone flies with $x(t) = 4.0\,t$ and $y(t) = 3.0\,t$ (meters, seconds): trajectory the line $y = \tfrac34 x$, velocity $\vect v = (4.0, 3.0)$ at all times, speed $\sqrt{4.0^2 + 3.0^2} = 5.0\,\mathrm{m}/\mathrm{s}$, constant.

Example 24.10 (Braking distance)

A car at speed $v_0$ brakes with constant deceleration $a$ (acceleration $-a$). It stops when $v(t) = -a t + v_0 = 0$, at $t_s = v_0/a$, having covered $d = -\tfrac12 a t_s^2 + v_0 t_s = v_0^2/(2a)$. The square is the road-safety headline: doubling the speed quadruples the braking distance — with $a = 6.0\,\mathrm{m}/\mathrm{s}^{2}$, $16\,\mathrm{m}$ from $50\,\mathrm{km}/\mathrm{h}$, $64\,\mathrm{m}$ from $100\,\mathrm{km}/\mathrm{h}$.