How to Choose the Right Kinematics Equation: A SUVAT Decision Guide

Stop guessing which kinematic equation to use. This decision guide shows how to pick the right SUVAT formula from the one variable you are missing, with a worked example, the mistakes that cost marks, and free calculators for each step.

Four Equations, One Decision

Every constant-acceleration problem draws on the same four equations, so the hard part is never the algebra. It is choosing which equation to start with. Most lost marks come from picking a formula that contains a variable the question never gave you, then going in circles trying to find it.

There is a single rule that removes the guesswork: identify the one SUVAT variable the question neither gives you nor asks for, and use the equation that leaves it out.

The Five SUVAT Variables

  • s — displacement, in metres. The straight-line distance from start to finish, not the total path travelled.
  • u — initial velocity, in metres per second. The speed and direction at the moment timing starts.
  • v — final velocity, in metres per second. The speed and direction at the moment timing stops.
  • a — acceleration, in metres per second squared. Assumed constant throughout.
  • t — time, in seconds. The interval between the two velocity measurements.

    • Each of the four equations uses exactly four of these five variables. That single fact is the entire basis of the decision rule.

    The Decision Rule: Name the Missing Variable

    Read the question twice. List what you are given, then underline what you are asked for. Whichever of s, u, v, a and t is left over is your missing variable, and exactly one equation omits it.

    Missing v? Use s = ut + ½at²

    Reach for this when the question gives you a starting velocity, an acceleration and a time, then asks how far the object travelled. A car pulling away from traffic lights, a stone dropped from a bridge, a train braking over a known interval — none of these need the final velocity to answer.

    Missing s? Use v = u + at

    The simplest of the four, and the one to use when displacement never appears in the question. If you are asked how fast something ends up after accelerating for a given time, this is a one-line answer.

    Missing t? Use v² = u² + 2as

    The most commonly forgotten equation, and the one that saves the most work. When a question gives you a distance and asks for a velocity, or the reverse, without ever mentioning time, this equation avoids a two-step detour through t.

    Missing a? Use s = ½(u + v)t

    Useful when acceleration is unknown or simply irrelevant. Because ½(u + v) is the average velocity under constant acceleration, this equation is really distance = speed × time in disguise.

    A Worked Example

    A cyclist travelling at 4 m/s accelerates uniformly at 1.5 m/s² over a distance of 30 m. What is the final velocity?

    You are given u = 4 m/s, a = 1.5 m/s² and s = 30 m, and asked for v. The leftover variable is t, since time is neither given nor requested, so the equation that omits time is the one to use.

    v² = u² + 2as = 4² + 2(1.5)(30) = 16 + 90 = 106, so v = √106 ≈ 10.3 m/s.

    Had you started with v = u + at instead, you would have needed t first, turning a single calculation into two and doubling your chances of a rounding error.

    Four Mistakes That Cost Marks

  • Treating distance and displacement as the same quantity. An object that returns to its starting point has travelled a distance but has zero displacement, and every SUVAT equation uses displacement.
  • Dropping the sign on deceleration. If forward motion is positive, braking must enter the equation as a negative acceleration. Sign errors are the most common cause of impossible answers.
  • Mixing units before substituting. Convert kilometres to metres and hours to seconds first, not halfway through the working.
  • Forgetting that v² = u² + 2as has two roots. Take the one whose direction matches the motion described in the question.

    • When SUVAT Stops Applying

    Every equation above assumes acceleration is constant. That assumption fails in three common situations, and using SUVAT anyway produces a confidently wrong answer.

  • Air resistance is significant, so acceleration falls as speed rises.
  • The force changes with position, as it does for a mass on a spring.
  • The motion is two-dimensional, such as a launched projectile.

    • The projectile case has a workaround worth knowing. Horizontal and vertical motion are independent, so you can apply SUVAT separately to each axis, with a = 0 horizontally and a = g vertically.

    Check Your Method, Not Just Your Answer

    Once you know which equation you need, verifying the arithmetic should be quick. These calculators show the substituted formula alongside the result, so you can confirm your method as well as your number.

  • Kinematics calculator — solves any of the four equations for whichever variable you are missing.
  • Velocity calculator — for the v = u + at case and straightforward speed problems.
  • Acceleration calculator — when a is the unknown rather than a given.
  • Displacement calculator — for s = ut + ½at² and average-velocity problems.
  • Projectile motion calculator — splits a two-dimensional launch into independent axes.
  • Kinetic energy calculator — the natural next step once you have solved for v.

    • The decision rule takes a few problems to become automatic, but it is worth the practice. Naming the missing variable turns a choice between four equations into a choice between one.

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