Body under Constant Acceleration

Theorem

Let $B$ be a body under constant acceleration $\mathbf a$.

The following equations apply:

$(1):$ Velocity after Time

$\mathbf v = \mathbf u + \mathbf a t$

$(2):$ Distance after Time

$\mathbf s = \mathbf u t + \dfrac {\mathbf a t^2} 2$

$(3):$ Velocity after Distance

$\mathbf v \cdot \mathbf v = \mathbf u \cdot \mathbf u + 2 \mathbf a \cdot \mathbf s$

where:

$\mathbf u$ is the velocity at time $t = 0$

$\mathbf v$ is the velocity at time $t$

$\mathbf s$ is the displacement of $B$ from its initial position at time $t$

$\cdot$ denotes the dot product.

Also known as

The equations defining the behaviour of Body under Constant Acceleration can often be seen collectively referred to, particularly at elementary and high school levels, as SUVAT, for the usual symbols used to represent the quantities involved.

Sources

• 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): constant acceleration