선택 방법 the Right 운동학 Equation: A SUVAT Decision Guide

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

Four Equations, One Decision

Every constant-가속도 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 공식 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 guess일: 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 — 변위, in metres. The straight-line distance from start to finish, not the total path travelled.
  • u — initial 속도, in metres per second. The 속력 and direction at the moment timing starts.
  • v — final 속도, in metres per second. The 속력 and direction at the moment timing stops.
  • a — 가속도, in metres per second squared. Assumed constant throughout.
  • t — time, in seconds. The interval between the two 속도 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 속도, an 가속도 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 속도 to answer.

    Missing s? Use v = u + at

    The simplest of the four, and the one to use when 변위 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 일. When a question gives you a distance and asks for a 속도, 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 가속도 is unknown or simply irrelevant. Because ½(u + v) is the 평균 속도 under constant 가속도, this equation is really distance = 속력 × time in disguise.

    A 일ed 예제

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

    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 점수를 깎는 실수

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

    • When SUVAT Stops 적용ing

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

  • Air 저항 is significant, so 가속도 falls as 속력 rises.
  • The 힘 changes with position, as it does for a 질량 on a spring.
  • The motion is two-dimensional, such as a launched projectile.

    • The projectile case has a 일around 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.

    확인 Your Method, Not Just Your 답

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

  • 운동학 calculator — solves any of the four equations for whichever variable you are missing.
  • 속도 calculator — for the v = u + at case and straightforward 속력 problems.
  • 가속도 calculator — when a is the unknown rather than a given.
  • 변위 calculator — for s = ut + ½at² and average-속도 problems.
  • Projectile motion calculator — splits a two-dimensional launch into independent axes.
  • 운동 에너지 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.

    문서

    • 탄성 위치 에너지 공식 (U = ½kx²): 계산기 & 예제
    • 계산 방법 전기 전력 (P = VI, I²R, V²/R)
    • 계산 방법 파동 속도 (v = fλ): 주파수 × 파장
    • 계산 방법 무게 (W = mg): 질량 vs 힘
    • 계산 방법 밀도 (ρ = m/V): 질량 ÷ Volume
    • 계산 방법 가속도 (a = (v − u)/t)

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