SUVAT Equations (AQA AS Physics): Revision Note

SUVAT equations

• The SUVAT equations are the equations of motion used for objects in constant acceleration

• They contain the following variables:

  • $s$ = displacement (m)

  • $u$ = initial velocity (m s^-1)

  • $v$ = final velocity (m s^-1)

  • $a$ = acceleration (m s^-2)

  • $t$ = time (s)

• The four SUVAT equations are:

$v=u\hspace{0.17em}+at$

$s=ut+\frac{1}{2}a{t}^2$

$s=\left(\frac{u\hspace{0.17em}+v}{2}\right)t$

$v^2=u^2\hspace{0.17em}+2as$

• These are all given on the data sheet

• All the variables, apart from time t, are vector quantities

  • This means they can either be positive or negative depending on their direction

• The key terms to look out for are:

  • 'Starts from rest', or if the initial velocity is not mentioned, this means u = 0

  • 'Starts from rest' means an object starts from rest at x = 0 when t = 0

  • If an object is only 'falling due to gravity' then a = g = 9.81 m s^-2

  • It doesn't matter which way is positive or negative for the scenario, as long as it is consistent for all the vector quantities

    • For example, if downwards is negative then for a ball travelling upwards, s must be positive and a must be negative

• SUVAT equations are used for motion with constant acceleration in a straight line

  • For example, an object falling in a uniform gravitational field without air resistance

How to use the SUVAT equations

• Step 1: Write out the variables that are given in the question, both known and unknown, and use the context of the question to deduce any quantities that aren’t explicitly given

  • e.g. for vertical motion a = ± 9.81 m s^–2, an object which starts or finishes at rest will have u = 0 or v = 0

• Step 2: Choose the equation which contains the quantities listed in Step 1

  • e.g. the equation that links s, u, a and t is $s=ut+\frac{1}{2}a{t}^2$

• Step 3: Convert any units to SI units and then insert the quantities into the equation and rearrange algebraically to determine the answer

• Sometimes the question may have to be split into two, where the SUVAT equations will have to be used twice

  • For example, if there are two masses connected over a pulley and one mass continues moving after the other has stopped