Metre per second squared (m/s²): unit of acceleration

Physical interpretation

Acceleration is a vector quantity: it has both magnitude (how rapidly speed changes) and direction (which way the velocity changes). The unit m/s² quantifies the magnitude. For example, if a car accelerates uniformly at 2 m/s² from rest, after one second its speed will be about 2 m/s, after two seconds about 4 m/s, and so on. Negative values of m/s² are commonly used to indicate deceleration (a reduction in speed) or acceleration in the opposite direction.

Notation, related units, and simple conversions

In formal notation m/s² is equivalent to m·s⁻². It is the SI-derived unit obtained from base units (metre and second). Common comparisons include the acceleration due to Earth's gravity, often denoted g, which is approximately 9.81 m/s² and is used as a reference for weight and free-fall problems. Other units sometimes seen are centimetres per second squared (cm/s²) and kilometres per hour per second (km·h⁻1·s⁻1), which can be converted to m/s² by using the appropriate scale factors.

Practical examples and applications

Values expressed in m/s² appear throughout mechanics, engineering, biomechanics and vehicle testing. Typical examples:

• A freely falling object near Earth experiences about 9.81 m/s² downward (ignoring air resistance).
• Pedestrian walking acceleration might be a fraction of 1 m/s²; a sprint start can reach several m/s² briefly.
• Braking performance of vehicles and ride comfort in elevators or theme-park rides are assessed using accelerations in m/s².

Historical and practical notes

The metre per second squared arose naturally when classical mechanics formalized motion as change of velocity per time. Using SI units keeps equations in mechanics simple: Newton's second law, F = ma, uses metres, seconds and kilograms so that force is in newtons when acceleration is in m/s². Instrumentation such as accelerometers directly reports measurements in m/s² or in multiples of g; careful calibration and orientation are required because acceleration sensors respond to both inertial accelerations and to gravity.

Distinctions and common pitfalls

Do not confuse speed (a scalar measured in m/s) with acceleration (a vector in m/s²). Also be cautious converting units that mix time scales (for example, km/h per second) — always apply consistent conversion factors to reach m/s². Lastly, observed accelerations often vary with time; the unit m/s² applies equally to constant (uniform) acceleration and to instantaneous acceleration defined as the derivative of velocity with respect to time.

For further reading about units and standards see general references on SI units and introductory mechanics: SI unit overview, acceleration, speed and velocity, time units.