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SUVAT equations - Wikipedia, the free encyclopedia

SUVAT equations

From Wikipedia, the free encyclopedia

The SUVAT equations are five basic equations used to describe motion of a classical system under constant acceleration. They are named SUVAT equations after the five variables that they contain.

[edit] Variables

There are five variables used in the SUVAT equations. Each of the five equations uses all but one of these variables. The variables and their dimensions are given below.

  • \mathbf{s} Displacement. Units of m (meters, i.e distance from start).
  • \mathbf{u} Initial velocity. Units of ms − 1 (meters per second, i.e speed and direction).
  • \mathbf{v} Final velocity. Units of ms − 1 (meters per second, i.e speed and direction).
  • \mathbf{a} Acceleration. Units of ms − 2 (meters per second squared, i.e rate of change of speed, and direction).
  • t Time. Units of s (seconds, i.e an amount of time).

Note that all variables besides time are vectors, as they have a direction as well as magnitude.

[edit] Equations

The individual SUVAT equations are listed below. It is important to remember that these equations only work in situations involving constant acceleration. For non-constant acceleration, calculus must be used.

\mathbf{v} = \mathbf{u} + \mathbf{a}t \,
\mathbf{s} = \mathbf{u}t + \frac{\mathbf{a}t^{2}}{2}\,
\mathbf{s} = \mathbf{v}t - \frac{\mathbf{a}t^{2}}{2}\,
\mathbf{v}^{2} = \mathbf{u}^{2} + 2\mathbf{a}\cdot\mathbf{s}\,
\mathbf{s} = \frac{\mathbf{u} + \mathbf{v}}{2}t\,

[edit] See also

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