Speed vs Velocity
Speed and velocity are often used interchangeably in everyday language, but in physics they have distinct meanings. Speed is a scalar quantity — it has only magnitude. Velocity is a vector — it has both magnitude and direction. A car driving in a circle at constant 60 km/h has constant speed but constantly changing velocity (because direction changes). Average speed = total distance traveled / time; average velocity = displacement (straight-line change in position) / time.
The SUVAT Equations
The five SUVAT equations describe motion under constant acceleration. Each equation connects four of the five kinematic variables (s, u, v, a, t), omitting one. They were derived by Galileo and systematized by later physicists. Key equations: v = u + at (no displacement), s = ut + ½at² (no final velocity), v² = u² + 2as (no time). When given any three variables, you can always solve for the other two.
Converting Speed Units
The key conversion factors: 1 m/s = 3.6 km/h = 2.237 mph = 3.281 ft/s = 1.944 knots. A knot is exactly 1 nautical mile per hour (1.852 km/h), used in aviation and maritime contexts. Mach number (M = v/c, where c is the speed of sound) varies with altitude and temperature — at sea level (15°C), Mach 1 = 340.3 m/s. At 10 km altitude (−50°C), Mach 1 = 299.5 m/s.
Stopping Distance
Total stopping distance = reaction distance + braking distance. Reaction distance = v × t_reaction. Braking distance = v²/(2a), where a is deceleration. Since braking distance depends on v², doubling speed quadruples the braking distance. A car going 100 km/h needs 4× the braking distance of one going 50 km/h — a critical safety insight explaining why speed limits exist near schools and pedestrian crossings.