Displacement, velocity and acceleration

Displacement, velocity and acceleration are vectors: each has a direction as well as a size, unlike the distance and speed used at a lower level.

Practise this concept

Displacement, velocity and acceleration are the vector upgrades of distance, speed and — well, acceleration doesn't really have a scalar cousin, but the same idea applies. Each one tracks not just how much but which way.

A car that drives 3 km east then 3 km west back to its starting point has covered a distance of 6 km, but its displacement is zero — it ended up exactly where it began. Distance only ever grows; displacement can shrink, cancel out, or even come back to zero.

Acceleration is any change in velocity, not just a change in speed. An object moving at constant speed around a circular track is accelerating the whole time, because its direction is constantly changing even though its speed never does. This is the detail that trips people up most: "constant speed" does not mean "constant velocity," and it certainly doesn't mean "zero acceleration."

Key ideas

Requires: Speed and motion, Scalars and vectors

Unlocks: Newton's first law, Newton's second law, Projectile motion, Uniform circular motion

Formulas

v = u + at

Symbol	Name	Unit
$v$	velocity	m/s (metre per second)
$u$	velocity	m/s (metre per second)
$a$	acceleration	m/s^2 (metre per second squared)
$t$	time	s (second)

Common misconceptions

Displacement and distance are always equal in magnitude.
An object with zero velocity cannot be accelerating.
If velocity is constant, the object must have some acceleration keeping it that way.

Resources

Articles

Part of these UT courses

This concept is mapped as covering part of the following course(s) in the University of Tartu curriculum.

The physical world viewLOFY.01.002
Materials physics practical I — mechanics and heatLOFY.02.055
Physics practical I — mechanics and heatLTFY.01.004
Mechanics and heatLTFY.01.006
Analytical mechanicsLTFY.04.016