Physics · Kinematics and motion

There are five suvat equations. How do I know which one a question wants?

AS and A Level 2 min read Worked answer

You never have to choose from five. List what you have, list what you want, and exactly one equation will contain those and nothing else. Picking is a process, not a judgement, and students who treat it as a judgement lose time they do not have.

Do this before writing anything

Write the five letters down the margin of your working:

s   displacement
u   initial velocity
v   final velocity
a   acceleration
t   time

Go through the question and put a number next to every one it gives you. Put a question mark next to the one it asks for. You will almost always have three knowns and one unknown.

Now look at which letter has nothing beside it. That is the variable you do not care about, and the right equation is the one that leaves it out.

Which equation leaves out what

Equation Missing
v = u + at s
s = ut + ½at² v
s = vt − ½at² u
v² = u² + 2as t
s = ½(u + v)t a

That table is the whole skill. If the question gives you u, a and t and wants s, then v is the one with nothing beside it, so you want the equation missing v: s = ut + ½at².

The two things that actually cost marks

Signs. Choose a positive direction before you start and write it down. Then every quantity gets a sign consistent with it. For an object thrown upwards with downward-positive, u is negative and a is +9.81. Mixing the convention halfway through a question is the single most common way a correct method produces a wrong answer, and it is invisible when you check your own work because you re-read it with the same assumption you made the first time.

Splitting the motion. suvat only applies while acceleration is constant. A ball thrown up and caught has constant acceleration throughout, so one calculation works. A car that accelerates, cruises, then brakes does not: that is three phases and three separate calculations, joined by the fact that the final velocity of one is the initial velocity of the next. Trying to force one equation across a changing acceleration is a guaranteed zero.

A check worth doing

Once you have an answer, ask whether it is physically sensible. A time of −3 seconds usually means you dropped a sign. A displacement larger than the building the object fell from means you used the wrong value for something. Ten seconds of sanity checking catches most of the errors that survive the algebra, and examiners award the method marks either way, so showing the working and then correcting yourself still scores.

Working from a past paper? Mark your attempt against the published mark scheme before reading an answer like this one. Finding out where you lost the marks is worth more than seeing a correct solution, because the correct solution rarely tells you what you did instead.

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