Displacement from average velocity

What the symbols mean

$s$

the displacement in metres: distance in a chosen positive direction (it can be negative) (m)

$u$

the initial velocity in m/s (m/s)

$v$

the final velocity in m/s (m/s)

$t$

the time in seconds (s)

When to use it

Use it with constant acceleration when the acceleration itself is unknown and not needed: a car going from 10 m/s to 30 m/s in 4 s, a train braking to a stop. It is the SUVAT equation without a. It does not hold if the acceleration changes during the motion.

Why it works

The velocity–time graph is a straight line, so the area under it is a trapezium with parallel sides u and v and width t: $\frac{1}{2}(u+v)t$.

Common mistakes

• Using it when acceleration is not constant; the average velocity is then not $(u+v)/2$.
• Forgetting to halve the sum of the velocities.