Equations of motion

\(\text{average velocity} = \dfrac{\text{displacement}}{\text{time}}\)

\(\text{acceleration} = \dfrac{\text{final velocity}-\text{initial velocity}}{\text{time}}\)

For the movement of an object in a straight line with constant acceleration, the following letters are used:

\(s\) for displacement
\(u\) for initial velocity
\(v\) for final velocity
\(a\) for acceleration
\(t\) for time

These are used for the so-called suvat formulae:

\(v = u + at\)

\(s = ut + \frac{1}{2}at^2\)

\(s = \frac{1}{2}(u+v)t\)

\(v^2 = u^2 + 2as\)

\(s = vt - \frac{1}{2}at^2\)

To use these formulae, write down the known variables from the question. The question will tell you at least 3 variables out of the 5. Identify the appropriate equation to use for solving the unknown variables.

Vertical motion under gravity

suvat formulae can also be used to model vertical motion under gravity.

For a falling object, acceleration towards the Earth is constant (ignoring air resistance) and is equal to the gravitational constant \(g\) (\(\approx 9.81~m~s^{-1}\)).

For an object being thrown upwards vertically, it will have a negative acceleration equal to \(-g\) (again ignoring air resistance).