Speed, Velocity and Acceleration

How fast something is moving sounds like a simple question, but physicists have three different words for it: speed, velocity and acceleration. They sound alike, but each tells you something subtly different. Speed is how fast you are going. Velocity is how fast AND in what direction. Acceleration is how quickly your velocity changes. Get all three right and you can describe almost any kind of motion, from a snail crawling to a rocket leaving Earth.

  • SpeedHow fastNo direction
  • VelocityHow fast AND directionA vector
  • AccelerationChange of velocity per secondSpeeding up, slowing down or turning
  • Speed unitMetres per second (m/s)Or km/h, mph
  • Acceleration unitm/s2Metres per second squared
  • Earths gravity acceleration9.8 m/s2Roughly 22 mph per second

Speed

Speed is how far you travel in a given time. The formula is:

speed = distance / time

If you walk 1 km in 10 minutes, your speed is 6 km/h. If you cycle 20 km in 1 hour, your speed is 20 km/h. Speed is what your speedometer measures in a car.

Common units of speed:

  • Metres per second (m/s): physicists favourite.
  • Kilometres per hour (km/h): everyday in the UK and most of Europe.
  • Miles per hour (mph): UK road signs and US standards.
  • Knots: nautical speed, used by ships and planes.

Velocity

Velocity is speed with direction included. So:

  • A car driving north at 50 km/h has a velocity of 50 km/h north.
  • The same car driving south at 50 km/h has a velocity of 50 km/h south.
  • Both have the same speed, but different velocities.

Why does direction matter? Because if you change direction, your velocity changes even if your speed stays the same. A car driving in a circle at constant 30 km/h has constantly changing velocity. This matters because changing velocity always means acceleration, and acceleration always means a force is acting.

Fact A vehicle going round a corner is technically accelerating, even if the speedometer never changes. Acceleration in physics means any change in velocity, including a change in direction. The force needed to turn the corner is what makes you lean sideways or feel pushed against the door of the car.

Acceleration

Acceleration is how quickly the velocity changes. Speeding up, slowing down or changing direction are all forms of acceleration.

  • Acceleration is measured in metres per second squared (m/s2).
  • If a car goes from 0 to 20 m/s in 4 seconds, its acceleration is 5 m/s2.
  • That means its velocity increases by 5 m/s every second.

Slowing down is just acceleration in the opposite direction to motion. Sometimes called deceleration, but to a physicist it is still acceleration (with a negative sign).

Famous accelerations

  • Free fall on Earth: 9.8 m/s2 downward. After 1 second of falling, you are moving at 9.8 m/s (about 35 km/h).
  • Family car at full throttle: 3 to 5 m/s2.
  • Sports car at full throttle: up to 9 m/s2 (about 1g).
  • Formula 1 car braking: up to 50 m/s2 (about 5g).
  • Space rocket at takeoff: typically about 3g for crew comfort.
  • Fighter pilot in a tight turn: can briefly reach 9g (pilots may pass out without anti-g suits).
  • A car crash from 100 km/h to standstill in 0.1 s: about 28g; usually fatal without restraint.
Did you know? When you hear a fast cars stats like "0 to 60 mph in 3 seconds", that is the cars acceleration. Going from 0 to about 27 m/s in 3 seconds is an acceleration of about 9 m/s2: just about equal to Earths gravity. That is why your body feels almost as if it weighs an extra 1g while the car accelerates that fast.

How to measure each one

  • Speed: speedometer in a car. Or simply measure how far you go over a known time (rugby pitch length divided by stopwatch time).
  • Velocity: a speedometer plus a compass. GPS units calculate velocity continuously.
  • Acceleration: accelerometers (small electronic sensors). Smartphones contain one for screen rotation and step-counting.

Why this matters

The difference between speed, velocity and acceleration matters anywhere motion is important:

  • Engineering: building bridges, cars, lifts and rollercoasters all need careful acceleration calculations.
  • Sports: an athletes top speed matters, but so does their acceleration.
  • Vehicle safety: cars are tested for crash performance, which is essentially measuring how sudden the change in velocity (acceleration) is during a crash.
  • Space travel: rockets must accelerate carefully to avoid crushing the crew and to reach orbit safely.
  • Weather and traffic: how fast the wind blows or how cars build up speed on a motorway uses the same physics.
Try this Time yourself walking a measured distance (say 100 metres). Distance / time gives your speed. Then time how long it takes you to go from a standstill to a steady running speed: that lets you estimate your acceleration. (For example, going from 0 to 5 m/s in 2 seconds is an acceleration of 2.5 m/s2.) Look at the result and notice how human acceleration is typically only a fraction of Earths gravitational acceleration (9.8 m/s2).
Deeper dive: why g-forces matter for pilots and astronauts

One way to talk about big accelerations is to compare them to Earths gravity (g). 1g is the normal gravitational acceleration: 9.8 m/s2.

  • Standing still on Earth = 1g (your body weight pressing on your feet).
  • Sitting in a parked car = 1g.
  • A fast rollercoaster drop or take-off in a rocket = 3 to 4g (you feel several times heavier than normal).
  • A fighter jet in a tight turn = 5 to 9g.
  • A car crash without seatbelts = 30g or more (typically fatal).

The human body has limits. Up to about 4g, most healthy people feel uncomfortable but unharmed. Above 5g, blood starts to drain from the brain to the feet (because your "weight" has grown), causing dimming of vision. At 6 to 9g, untrained pilots lose consciousness (a "G-LOC", or g-induced loss of consciousness). Even fit pilots usually pass out above 9g without help.

To help fighter pilots and astronauts cope, engineers have invented:

  • G-suits: pressurised trousers that squeeze the lower body when g-forces rise, helping push blood up to the brain.
  • Reclining seats: keeping the body level with the direction of acceleration spreads the load along the body, making more g-force tolerable.
  • Special breathing techniques: pilots learn to grunt and squeeze their abdominal muscles to keep blood pressure up during high-g turns.

Astronauts during the Apollo missions experienced 4 to 6g during launch and 6 to 7g during re-entry. Modern crewed missions are designed to limit acceleration to about 3 to 4g, since astronauts spend so long in microgravity that they become less tolerant to g-forces. Acceleration is one of the practical limits on how fast humans can travel through space.

For more, see Newtons three laws of motion and momentum.